Excellent video by Dr. Wildberger explaining why concept of "real numbers" is rotten.
I second his call to research the sociology and history of these ideas, so we can put mathematics on sounder foundations.
YouTube Pure mathematics relies on a fake arithmetic | Sociology and Pure Mathematics | N J Wildberger Number systems are at the heart of mathematics --- and have been for at least 4000 years. The Egyptians' had a base 10 system that used fractions, albeit n... What does he think pi and e and sqrt(2) are if they're not numbers?
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13bJsMyjiNF21qYTLK5tZizwEovpT6DNeu VerifiedI can't speak for him, but I'd say they are formulas for the construction of numbers, not numbers themselves.
As you run more iterations of the formula, the number that's generated slightly changes / gets additional decimals added to it.
So, there's no fixed quantity that equals "the square root of two."
Instead, there's a symbol that represents a formula for the generation of numbers.
The generated numbers begin with 1.41 and get more decimals added with more cycles.
Well there definitely is a fixed quantity. You just can't write it out all at once.
Why "definitely"? Mathematics is a language, and just like any language, the symbols don't necessarily correspond to some independently existing part of the universe.
What explanatory benefit do you gain from saying the sqrt(2) is a fixed quantity?
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