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Formalising a new proof that the square root of two is irrational

lawrencecpaulson.github.io

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Re: Formalising a new proof that the square root of two is irrational

#91

Post by thaumasiotes »

BeetleB wrote: post #89
thaumasiotes wrote: post #87

Earlier quoted context omitted.

Textbooks aren't that bad. Here's what Pearson's Algebra 1 says when introducing the novel concept of the radical sign: > The radical symbol √ indicates a nonnegative square root, also called a principal square root . I quoted that one because it's available on libgen ( http://library.lol/main/BE522034F8D3680B248162CD2C35D455 , page 16), but obviously every basic algebra textbook covers this. The symbol is never disc…

Your evidence is consistent with my claims. Or rather: I never claimed there aren't textbooks that define it as the positive square root.

All textbooks define it that way. There is no other definition available for that symbol.

Re: Formalising a new proof that the square root of two is irrational

#92

Post by orra »

nanis wrote: post #90
orra wrote: post #8

Earlier quoted context omitted.

You keep saying “author”, but putting a screenshot of a Tumblr post on Twitter is stretching the word quite considerably. Besides, the Tumblr post is already a secondary source.

We do not know what was in the tweet simply because it is not referenced/cited.

Okay, but that's not a reason to jump to the conclusion of bad citation practices.

Re: Formalising a new proof that the square root of two is irrational

#94

Post by graycat »

tromp wrote: post #20
graycat wrote: post #18

Let's have a simple proof so that we don't have to argue about more complicate issues: For integers p, q with q not 0, suppose 2 = (p/q)^2 Then 2 q^2 = p^2 and the left size has an odd number of factors of 2 and the right side has an even number of factors of 2, a contradiction. Therefore such p, q do not exist, and 2 does not have a rational square root. Done.

It is simple if you can assume unique factorization of positive integers [1]. [1] https://en.wikipedia.org/wiki/Fundamental_theorem_of_arithme...

> It is simple if you can assume unique factorization of positive integers [1].

Since the fundamental theorem of arithmetic is a classic and fundamental pillar of math, in writing math is it not appropriate to say "if you can assume".

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