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

Re:Formalising a new proof that the square root of two is ir... by thaumasiotes on Thursday January 19, 2023 @03:08PM (#34444959)

That is not what people are taught. If that were true, the numerator in the quadratic equation would be "-b + √(b² - 4ac)", not "-b ± √(b² - 4ac)".

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Re:Formalising a new proof that the square root of two is ir... by BeetleB on Thursday January 19, 2023 @04:34PM (#34445931)

Your statement assumes the educational system values consistency, which is a clearly false assumption.

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Re:Formalising a new proof that the square root of two is ir... by thaumasiotes on Thursday January 19, 2023 @06:41PM (#34447245)

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 discussed -- or used -- in any other terms than that it uniquely refers to a positive square root.

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Re:Formalising a new proof that the square root of two is ir... by BeetleB on Thursday January 19, 2023 @07:58PM (#34447826)

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

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Re:Formalising a new proof that the square root of two is ir... by thaumasiotes on Friday January 20, 2023 @02:46AM (#34450231)

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

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