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Twice in Minnesota a black with a legal firearm was murdered by police with no consequences for the police. The right to a firearm is not, in practice or in law, at all similar to the right of free speech. The government, with impunity, murders legally armed people. It’s not really a right when people of the wrong race or creed get killed for being armed.

Gun control will quickly occur once black men arm themselves and the courts will concur. Similar to how religious freedom arguments get ignored when the Satanic Church makes them.


"Gun control will quickly occur once black men arm themselves"

Are you really that ignorant about current gun ownership patterns in the US (OK, the biggest new group is black women, but...)? How many black men in Chicago for example use their legally owned and Shall Issue concealed carry licenses to defend themselves, and everyone but people like you are cool with that, US V2.0 gun culture, the NRA which is more V1.0, the local authorities etc.? It doesn't even count as more than local news, except we RKBA activists try to collate all such reports.

"Similar to how religious freedom arguments get ignored when the Satanic Church makes them."

Citations? Because I'm not getting the impression you have any knowledge of what's happening with the law and facts in the US at all. Except of course the government impunity through judge made "qualified immunity" and rigging of the game, which applies to all races and creeds. Ask us what we think about Eric Garner's fate while or in times past engaging in one of the oldest American traditions, unjust tax evasion.


You can find citations yourself. It’s easy to do.

When large numbers of black men walk around with AR-15s there will be calls for gun control. The last time black men overtly armed themselves in 70s there was a call for gun control. Reagan even called for gun control when that happened.


"When large numbers of black men walk around with AR-15s there will be calls for gun control."

Again, you show your complete ignorance of the American situation, except of course for some responses to the Black Panthers et. al. in the Black Power era. But what you're also lacking along with religious freedom citations is knowledge of any laws passed as a result. Reagan didn't just "call" for gun control, he signed a bill to outlaw open carry and maybe more in the statehouse or whatever.

Strange thing, but you've also missed how attitudes towards blacks and other minorities in the US have evolved in the half century since then.


Can you please leave off with the snide 'are you really that ignorant' on every post and address people more respectfully, even if you disagree with them? Thanks.


It's an opportunely for them to prove they're not bald faced liars, or living in a bubble if in the US, or if outside the US as so many are, to admit they in fact do not know anything above the slogan level of the topics under discussion. In the face of calumniates that reach the point of blood libel, "disagree" is far too weak a word.

There is no respectful way to point out someone is either so ignorant they have no place in a discussion or are arguing in bad faith. For the general stuff, they just have to learn a few things, like how many blacks legally own arms, and how the vast majority of gun owners are entirely cool with that. For the specialized knowledge I've been providing my own citation as well as in other discussions pointers to for example the absolutely essential to know about Anti-Federalists.

And I'll ask you this personally: do you really believe someone who claims to believe "the Satanic Church" is legally discriminated against is worth doing anything other than asking for citations, which he refuses to provide?


Please, chill out and read the HN guidelines. This is a You problem. https://news.ycombinator.com/newsguidelines.html


That is not all the ruling implies or will lead too. You are badly distorting the impact this ruling will have.


The Constitution explicitly states well regulated militia and at the time the amendment was passed the lethality of guns was much less than it is today. The Supreme Court is on a clear path to destroy the mechanisms by which a modern state can function. We will soon live in a country where a legal act in one city will warrant the death penalty in another. A state that cannot adequately regulate weapons is not functional. What worked 250 years ago no longer works today.

The Constitution isn’t going to be changed because there is too much divisiveness. SCOTUS is doing what it can to foment this divisiveness. It’s time to be like Lincoln and ignore the Supreme Court. Strict adherence to words written 250 years ago is not a good way forward for the country. The U.S. is badly in need of reform for how its federal government works.


"The Constitution explicitly states well regulated militia"

As a subordinate clause; what follows is independent of it. Read the book I recommended in another comment for how it came about, as a political sop to those who wanted to flatly forbid standing armies and/or regulars, which those actually experienced in the Revolutionary War starting with the indispensable man Washington were not about to accept.

"and at the time the amendment was passed the lethality of guns was much less than it is today."

You ready to surrender your assault ink jet and laser printers?? For that matter, the lethality of the huge hunks of lead shot by the common muskets and rifles of the day was pretty serious.

"It’s time to be like Lincoln"

And there is goes, we get our war or we'll have a civil war.

Well, that's implicitly true in what you're saying, trying to confiscate the 600 million or so guns owned by the US people will most certainly result in another civil war. But you should think harder about this; to quote Glenn "Instapundit" Reynolds:

"Here’s the problem with public officials — because that’s really [Seidman’s] audience — deciding to ignore the Constitution: If you’re the president, if you’re a member of Congress, if you are a TSA agent, the only reason why somebody should listen to what you say, instead of horsewhipping you out of town for your impertinence, is because you exercise power via the Constitution. If the Constitution doesn’t count, you don’t have any legitimate power. You’re a thief, a brigand, an officious busybody, somebody who should be tarred and feathered and run out of town on a rail for trying to exercise power you don’t possess.

"So if we’re going to start ignoring the Constitution, I’m fine with that. The first part I’m going to start ignoring is the part that says, I have to do whatever they say."


Obviously, the reference to Lincoln was about him ignoring the Supreme Court and not a call to civil war. Your reading comprehension in this instance was quite bad.

One child was killed by jarts and they were banned. One person tried to blow up a plane with a shoe bomb and we all have to take off our shoes at the airport. But guns, let’s not ban those. Indeed let’s expand their prevalence.

If lethality and rate of gunfire being much higher today than 250 years ago is not a relevant point then why is it ok to ban machine guns? Shouldn’t I be able to protect my property with a tank or a flamethrower?

Pertaining to your comment on ink jet printers. When they are used for mass killings I’ll be willing to consider proposals for their regulation.


"As a subordinate clause; what follows is independent of it." Um... so your argument is that "when the writers of the Constitution explicitly wrote their reasoning for this clause, they didn't actually care if that reason mattered, they just felt like writing more words; and we can ignore half the sentence"? Followed shortly thereafter by lambasting people ignoring the Constitution?

...please tell me you see the irony here...


"they just felt like writing more words"

And now you're arguing in bad faith, I explicitly stated why the subordinate clause was part of the amendment and pointed you to a hard core reference for that. Not going to make any more replies to you.


At the time the Second Amendment was passed it was relatively common for private citizens to own artillery pieces that were far more lethal than modern small arms. We are a nation of laws. Your suggestion to ignore the law for the sake of expediency is horrifying, and that type of unprincipled and irresponsible attitude could lead to the downfall of our republic.


Accuracy, and reload times, etc. are much different for cannons today than they were 250 years ago. Population density is different and society is much more complex now. A well regulated militia means that the government has the right to regulate firearms. And a well regulated militia is no longer necessary for the defense of the country. The second amendment is obsolete and detrimental to the country.

We are not a nation of laws. We have seen our leaders try to overthrow the government with impunity. We have government agencies engage in torture and mass surveillance with impunity. We have police forces that kill legally armed people who have done no wrong with impunity. This is not a nation of laws as you put it. We have a Supreme Court ignore precedent and make up shit with its recent rulings. We recently had a President ignore the Constitution to enrich himself and nothing came of it. We have a Supreme Court decide that it wasn’t important to ensure that the votes for President were counted correctly and appointed Bush as the winner.

The Republic ended when a coup was attempted and nothing happened to the instigators. We will soon live in a country in which a legal act in one city is a death penalty crime in another. We soon will live in a country in which the government can’t meaningfully enforce administrative rules. It’s already over unless the Constitution is drastically rewritten or the Court in its present form is changed.


So what. None of those technical differences are relevant to restricting a fundamental right. The authors of the First Amendment didn't anticipate the Internet, but we don't use that as an arbitrary reason to restrict free speech. And you have completely misunderstood the meaning of "well regulated". Read the actual Supreme Court decisions.

Just because one person violated the Constitution doesn't give you the right to do the same. Two wrongs don't make a right.


The technical difference are fundamental. To interpret the intent of the writers one has to understand the world they lived in and not merely the words they wrote. “arms” in terms of lethality, ease of use, density of population, second order effects, type of society, etc. are much different now and the amendment is obsolete. Particularly since a well regulated militia is no longer necessary for the defense do the country. The tenth amendment is not enforced at all in terms of how it was written. It has morphed in terms of how it is interpreted since society grew much more complex. The second amendment needs to be dealt with similarly.

I didn’t say two wrongs make a right and didn’t use past violations of the Constitution as justification for anything. I just pointed out that the idea that we are a nation of laws is incorrect and that adherence to the Constitution is not done in a consistent way.

I understand the meaning of “well regulated” and I disagree with the Court’s interpretation of what that phrase means and how it should be interpreted. The Court is not infallible. Indeed, in recent times we see quite clearly how absurd it’s decisions can be. The Court should be ignored when it’s decisions are absurd. All decent governments rely on a consent of the governed and the Supreme Court has clearly overstepped itself in a slew of areas and it has lost its credibility. As such it’s recent decisions should be ignored.

If tomorrow the Court ruled that people have a right to create and use biological weapons I’m certain you’d say that the decision should be ignored. So don’t act as though the notion of ignoring the court is unthinkable or unprincipled or irresponsible. Particularly when there is historic precedent for doing so.


Nah. You're just making things up and obviously haven't done even a modicum of research on the historical context.


Clearly.


>the lethality of guns was much less than it is today

That's ludicrous, simply given the state of 21st century medicine vs 18th century medicine with respect to treatment of gunshot wounds alone.


Medicine improved, but so did the weaponry. You can't look at the medicine and ignore the increased efficiency and lethality of modern weapons.


Your perspective ignores human nature and how easily influenced people are at scale. Toyota did not put a gun to your head but American society long ago evolved to the point where having a car is a necessity for the vast majority of adults. The real issue is that the negative externalities for those design decisions decades ago have resulted in a lot of harm with little benefit.


In Saudi Arabia, Gulf States, and elsewhere in the region migrant workers have their passport taken by the employer and thus can’t leave the country. They are stuck. In most other countries the employer does not confiscate your passport. It’s weird to me that one needs a passport to leave a country. In the U.S. you don’t need a passport to leave.


Makes me think that the home countries are fairly complicit. Any country with robust consular services wouldn’t allow that to happen.

The US state department is happy to let governments know that US passports are property of the US government and may only be held under very limited circumstances. https://www.law.cornell.edu/cfr/text/22/51.7#:~:text=CFR-,%C....


If you’ve ever been to a GCC country, you’ll notice that passport control when leaving is extremely long. It’s filled with South Asian men (and some women) who are put through the ringer by the officials and often pulled aside for extra questioning before being able to board a flight. They all seem to be on pins and needles


That's not legal, and it doesn't happen in cases of the kind of workers you are talking about. Taking passport or treating to be accused of rape and similar things happen (not commonly) to domestic workers and drivers. In occasions they buy the right of Kafala from the Kafil for a couple of $1000s and you leaving before your contract ends feel to them like a loss of money, I would say the situation here is indeed similar to slavery. For industry workers, every worker is replaceable and the company hiring you has 0 incentive to force you to stay.

The real issue in gulf is not paying livable wages mainly. Anything else is comparable to farm workers in Europe.


According to the following link confiscating of passports is common in Bahrain for migrant workers.

https://www.hrw.org/news/2012/09/30/bahrain-abuse-migrant-wo...


It is in fact illegal to confiscate for a private entity to confiscate a passport in most Western countries.

Unfortunately it's not well policed, many hotels and office receptions try to do so when they issue you a badge but I always refuse.


you still need the passport to enter anywhere else, even your home country


A passport will allow you to go from anywhere in the world to anywhere else in the world and its usually hard to get.

"An emergency travelling document" will allow you to go from anywhere in the world to ONLY your home country and its usually easier to get.


>you still need the passport to enter anywhere else, even your home country

Your home country can't refuse you entry, regardless of identification. Deportees don't get to stay in the US just because they lost their passport.


They can (and often do, at least for deportations from the UK) demand to see evidence that the deportee is, in fact, one of their citizens. Which can be difficult to prove without a passport. We have people who have been in immigration detention for years because they won't cooperate in getting an emergency travel document, or their 'home' country doesn't accept that they have a right of admission there.


Assuming by free you mean universal coverage that is (almost) free at the point of usage then this is a solved problem. What the United States lacks in order to realize a solution is political willpower and an electorate that is savvy enough to know that wanting such a system does not make one a communist. (And that being a communist does not make one an evil person.)


...also the fact that the electorate generally can't out-compete the big money interests that lobby heavily to keep healthcare a private venture.

It's so easy to blame voters but the reality is that politics is about messaging, and how is the electorate supposed be savvy enough when these companies can spend unlimited amounts of money to keep us fighting each other about this stuff? Make no mistake, Google benefits from this depravity too.


It’s not the lobbyist. There is still a lot of people who don’t want universal healthcare because it might benefit “those lazy people who don’t want to work” and older people on Medicare who “want to keep the government out of healthcare”.


I don’t disagree in general with what you wrote. On the bogeyman of “socialism” I do blame the electorate. The irrational fear of anything remotely related to “socialism” in America has been going on far too long.


And that fear is stoked from the top down. You hear it all the time from the leadership of a certain political party. It's not just something that people fear naturally, it's driven home explicitly by the political messaging of those that benefit the most from our current system.


Yes, I know this. However, in this age of easy information and knowledge about other societies readily available it becomes more a matter of willful ignorance than being duped by propaganda.


You aren't familiar with the propaganda if you think folks duped by it would consider "other societies" with anything other than fear hatred and contempt. The problem with "do your own research" is confirmation bias.


What is the alternative? Counter-propaganda, my propaganda is better than your propaganda because mine is "right"?

I don't have a good answer to this question, I'm wondering if others do.


If I knew, I'd already be president? The only thing that seems to actually work is slow, one on one, patiently and empathetically working with people where they are. Mass media only seems to be effective at sowing division.

Maybe things were different under the Fairness Doctrine? I don't know.


Counter-propaganda isn't the answer. We've already got counter-propaganda, from the other political party. It's not persuading anybody who doesn't already drink that flavor of Kool-Aid.

No, I don't have an answer either. I just know that counter-propaganda isn't it.


Well, as I said, in my opinion people can be blamed given the readily available information and in regard to the multi-decade irrational fear of socialism. Willful ignorance is a thing.


Canada has "free" universal healthcare, but to call it a "solved problem" seems pretty naive.


The naivety is in thinking that if it doesn’t work in Canada then it must not be a solved problem. The naivety is in thinking that if you can find anecdotal evidence that in a particular instance Canada’s system worked worse than the U.S. system then it must be the case that Canada’s system is worse.

The U.S. per capita spends far more on healthcare than any other OECD country. We don’t get correspondingly better outcomes or coverage. Universal healthcare is a solved problem within the context that every system necessarily involves some sort of rationing since there aren’t enough medical resources in any country to do otherwise.

If you don’t want to use the phrase “solved system” then don’t but don’t pretend the U.S. is any way better other than in anecdotal instances. Below is a source for information on per capita spending for OECD nations. You can easily find information on health our outcomes, life expectancy, teen pregnancies, infant mortality, etc.

https://www.oecd-ilibrary.org/sites/876d99c3-en/index.html?i...


Sir, this is a Wendy’s.

I’m not sure how your reply has anything to do with what I said.

“Better than the US” is not some hurdle that makes a problem “solved”.

Canada is likely better at snow removal but that doesn’t make it a “solved problem”.


It’s a solved problem as far as one can get given the constraints involved. As I said, if you don’t want to use that phrase then don’t. I’m not going to quibble over semantics. Human societies are far more complex than programming and the notion of “solved” means something different in the former than in the latter. Use whatever phrase you want. Just don’t think the U.S. system is in any way better. You are the one who brought up an anecdotal experience in favor of the U.S. system over Canada’s system.


You keep talking about the US, but as a former resident of Canada I know that’s the country’s favorite measuring stick. “We’re not as bad as the US so stop complaining” is the favorite ring of politicians.

Doesn’t do much for the people disabled from pain on a 3 year wait list for a hip transplant or my buddy’s cousin’s kid who doesn’t get access to the standard of care of CF.

It’s not solved in the least, every country struggles, so using the word “solved” is, as I said, naive.


Perhaps you don’t understand how words work. Words can have different meanings/connotations depending on situation and context. As I said repeatedly, for me it is correct to say “solved” given the constraints involved. Human societies are complex and one can nitpick the world “solved” and say nothing is solved when it come policies of complex societies. So don’t use that word when it comes to societal issues. I and many others do use that word for certain issues. It’s naive of you to have your pedantic nitpicking on the word and not reflect on what it says about you. Obviously I keep bringing up the U.S. because that’s the context of my starting comment way above. And you yourself have brought up the U.S.

What goal do you wish to accomplish your pedantic nitpicking? You want to get others to believe that my views on national health policies are naive? You want me to realize that in a strict, mathematical sense of the word saying “solved” is incorrect? These are rhetorical questions because I’m not going to read your response. You clearly don’t know much about policy issues and what it means for a society have essentially “solved” an issue (or have found a decent enough solution that it isn’t a dire problem anymore so that some non pedantic people will say it is solved).

Carry forth Don Quixote on your quest to eradicate incorrect usage of what you think “solved” means.


Words have meaning and we should encourage people to use the right ones.

You claim I don’t know policy without knowing healthcare policy is my day job.

Even given the benefit of the doubt that as an outsider looking in you think it’s solved, but as someone who is elbow deep in it everyday “solved” just sounds naive.


It's a solved problem in the sense that it exists, and works[1] and it is available in a lot more places than Canada.

[1] "works" is an interesting point because it isn't clearly defined, and usually means different things to different people.

Ever experience of the system is "unique" - there is this mix of human patient with human provider with finite resources with medical knowledge with time. So there are plenty of examples of long waits, bad service, unfavorable outcomes, even death. It's not hard to cherry pick bad experiences here.

No health system will make everyone live forever. Death comes to us all sooner or late. But universal healthcare works in many places in raising the overall standard of public health, without bankrupting people in the process.

Given that its always spending limited money, and only scales at human rates, its far from perfect. But, at least for some, its better than a "health care level based on your wealth" system.


But the US isn't "healthcare based on your wealth".

You have Medicaid for the poor, heavily subsidized Obamacare for the people who don't get it through their employer (hello $100/month plan!) and Medicare for the retired.

I mean my cousin in the US whose kid has cystic fibrosis get better care through Medicaid than our other cousin in Canada who can't even get access to the latest drugs.


> heavily subsidized Obamacare for the people who don't get it through their employer (hello $100/month plan!)

That $100/month plan will include high deductibles and copays. A weekend visit to an urgent care for a kidney stone will still cost a couple hundred dollars out of pocket.


I don't think anyone that says this has actually been poor and needed medical care.


You just have to stay very poor. If you do anything to move up a little bit in life, the benefits stop and you are on your own.

https://www.verywellhealth.com/your-assets-magi-and-medicaid...


Being a communist absolutely makes you an evil person. About 5 times more evil than the group of people they fought against in a war.

As for socialized medicine it makes doctors another arm of the government. In the UK last week (or the week before) one arm of the government ordered another arm of the government to kill a 9 year old. We are also just outside a 2 year stretch of tyranny of governments all over the world giving that arm of government near unilateral power over our freedom at the point of a gun.


I hope you can break from the the intellectual shackles that bind you. I hope you can visit other countries and read from sources of information outside your comfort zone. Subscribing to a belief about which system of economics you prefer does not make one evil.


> Being a communist absolutely makes you an evil person.

Tell me you don't know what communism is without telling me you don't know what communism is.

Yes, every known communist country has been rife with fascism, authoritarianism, and corruption. But those are orthogonal with communism as an economic model. It's like saying socialism is evil because the Nazis were socialist (they really weren't) just because "Socialist" is part of "Nationalist Socialist Party" .

> In the UK last week (or the week before) one arm of the government ordered another arm of the government to kill a 9 year old.

[citation needed], because this sounds like an extremely gross misinterpretation of a situation, likely done deliberately in bad faith.


The Viet Cong were 5 times more evil than the USA?


I'm not convinced, even with the best of intentions. In fact, I am convinced of the opposite: A) Universal Health program would result in terrible quality health care B) It would lead to longer wait times, and less choices C) It would be insanely costly to fund. We've been busy printing a lot of $. Increased the Federal deficit from $21T to $30 since COVID and there isn't a good way to fund a bloated system in USA, comparisons with smaller nations is ridiculous and misleading.

We already have free health for the poor: https://en.wikipedia.org/wiki/Medicaid

> Medicaid is the largest source of funding for medical and health-related services for people with low income in the United States, providing free health insurance to 74 million low-income and disabled people (23% of Americans) as of 2017, as well as paying for half of all U.S. births in 2019.

What we should be doing is to fight the regulatory and bigpharma capture of US health system along with the horrible hospital + insurance racket. Google is now going to take advantage of the moat built by Big Gov and never ever allow anyone to compete.


Regarding (A) and (C), this is the obligatory reminder that:

* The US spends more public money on health care, per capita, than other wealthy nations, while also spending much much more private money than other wealthy nations

* By many measures, the US gets worse outcomes (e.g. life expectancy)

The conclusion that many draw from this is that perhaps a single-payer health care system in the US could dramatically lower private spending, also lower public spending, and perhaps improve outcomes. I don't personally know if that follows, but it's not implausible.

This is counter-intuitive to many, thus comments like your (A) through (C) are common, but might not be correct.

That said, I'm not aware of evidence that your (B) is wrong. That might be part of the trade-off.

As a non-American from America's hat, who has had a few (bigco-insurance-funded) run-ins with US Healthcare, my observations were that

* emergency health care at the no-expenses-spared level in the US was nicer than emergency healthcare up here, and I wouldn't want to pit my doctors vs those US doctors in a quality competition

* US doctors seemed really eager to waste money, like really eager, like it was creepy


> US doctors seemed really eager to waste money, like really eager, like it was creepy

Your last point is purely a function of the liability culture in the states. US physicians are quite aware of what's appropriate and what's inappropriate testing wise. However, as long as a physician can be held personally liable for any oversight - meaning that the results of an entire career can be lost - they're going to over-test.


Purely a function of liability culture? That seems like an extraordinary claim, your claim that there are no other causes. Do you have extraordinary evidence?

I'll note that I do have a few different bits of modest evidence to the contrary. But I wanted to focus my comment on concrete observations (both the large-scale statistical kind, and the personal anecdotal kind), rather than on speculation.


> * US doctors seemed really eager to waste money, like really eager, like it was creepy

I'd much rather a doctor "waste money" on a test than come up with an incorrect diagnoses based on symptoms only.


Wait times are just as bad in the US, and often worse, than other first world nations.


Maybe because the 2/3rds of the population is overweight or obese. It's like the education system in the US, you can spend all the money you want but if the participants aren't actively trying to improve...


> We already have free health for the poor: https://en.wikipedia.org/wiki/Medicaid

There are tens of millions of people who have no access to Medicaid because states chose not to expand it under the ACA, and there are plenty of poor people who make more than ~$16k a year, which is the cut-off for Medicaid.


> C) It would be insanely costly to fund.

How could it be even more expensive than our current inefficient, half-baked, worst of both worlds system, which is more expensive than socialized systems in other nations? And more expensive per capita, not simply overall.


More expensive per capita and still excludes millions of people who need healthcare but can't afford it.


> We already have free health for the poor:

No, we have free health insurance for some of the poor (states that have no accepted the ACA expansion have basically no coverage for adults without dependents.)

Medicaid is not (as a generality) free health care (it can be, in some states, for some recipients). It is free health insurance, which can have copayments, coinsurance, deductibles, etc.


I’m a bit confused on the choice part. Can you explain?

I think if someone can afford better, private care they should be able to. For example I would probably go to the universal healthcare family doctor but if I need a specific surgery I would like to be able to go to the best care I can get.


It appears as though you did not read the article. What the article describes cannot be attributed to booming stock market alone.


No, was merely pointing out that "make out" was the goal and the market was only one of the mechanisms. I assume insiders had far more interesting/significant methods, but the market was amazing and I assume related things like real estate also did well.


Typically before one gets to the point of really understanding how to prove things a fair amount of brain washing occurs. For instance, few people know why the distributive property holds but they use it all the time. Most people are comfortable with the idea that a negative real number times a positive real number is a negative real number but they can’t prove it. In order to prove these basic facts one needs a fair amount of what is called mathematical maturity.

The most basic subject to understand mathematical proofs is Euclidean geometry. There you will learn the basics of proofs and what it means to prove something.

Let’s look at x/a = b/c. You want to show that this equation has the same exact solution set as xc = ab. In order to prove this rigorously you’ll need to prove things about associativity. You’ll also need to prove that a unit isn’t a zero divisor in the real numbers. What we see is that to prove seemingly simple statements requires some machinery and to understand the necessity of this machinery requires mathematical maturity.

But maybe you don’t want to rigorously prove the above. Maybe you just want to understand why it is plausible that this is true. For that, pick up a beginning algebra book and actually read what it says and try to understand it. This is hard to do on your own.

Here’s a plausible explanation for why x/a = b/c has the same solution set as xc=ab. Note that a and c must be nonzero because we can’t divide by zero (this requires proof!). We note that

(x/a) times a

Is the same thing as x times (1/a times a). This is due to associativity. A nonzero number times it’s reciprocal is 1. And 1 times anything is itself. So x/a times a simplifies to x.

So,starting with

x/a = b/c

I can multiply both sides by a. I can do this since a is invertible and multiplying by an invertible element preserves equality (requires proof!). So what I get, after simplifying, is

x = (b/c) times a

I can rearrange things (by associativity) to write this as

x = (ab)/c

Now multiply both sides by c to get (I skipped a step by multiplying and simplifying at the same time)

xc = ab.


+1 for Euclidian geometry. Once you “prove” that you can find angle B and C knowing angle A it’s a pretty eye opening experience. This is why this is/was? emphasized in middle school geometry.


Any particular books you can recommend?


I disagree regarding Euclidean geometry. Euclid never does any proofs by induction, which is enough on its own to disqualify Euclid as a good introduction to proof.

What you want is a book that combines an introduction to logic with a bunch of different proofs from different areas of math, such as set axioms, relations, functions, sequences, construction of real numbers, etc. There are many books like this, here is one that includes all of that plus a little number theory and algebra towards the end: http://libgen.rs/book/index.php?md5=7E4D97D2F58B91D052595E68...


Euclids Elements


Similarly forall f x=y => f(x)=f(y) can do quite a lot of work given that you’re free to choose any convenient f and then substitute its body.


Thank you for that. It’s helpful. I suppose my next question is how do I attain mathematical maturity most efficiently?


One thing that will help a lot is being thorough. Try to understand as well as you can, try to fill in missing steps and details, make sure the text itself is actually clear and correct and is not missing something. Try to guess how a proof might start before looking at it.

Broadening your field of view will also help a lot. Some introductory abstract algebra (groups, rings, vector spaces) would be a solid next step in my opinion, because there you will have sets of axioms and lots of proofs and you will learn about properties such as commutativity, associativity, inverses and identities in a more abstract and general way.


Do you want something at the level of beginning algebra? Or something more advanced?


I know how to do beginning algebra and geometry but I don’t necessarily know why the various rote techniques work. So beginner as far as intuition. But also beginner for technique for things like linear algebra and calculus that I never learned at all.


There is a book called “Number, Shape, & Symmetry”. You can download it at z-lib.org. It’s a book that will give you the flavor of mathematics and prove some of the basic algebraic properties. It does not require calculus but will require a desire to understand. It’s an art form to read mathematics and understand. I recommend the book along with using a tutor or math.stackexchange.com.

Good luck!


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