Well there definitely is a fixed quantity. You just can't write it out all at once.
Post by twetch#1832
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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Well it doesn't change, does it? So how can it not be fixed?
Depends on what "it" is. The formula doesn't change, but the output of the formula does, depending on how many times you iterate.
1.41 is different than 1.414 is different than 1.4142, etc.
The formula stays the same. The output changes.
Ok, so? is sqrt(2) a quantity or is it the output of a formula? If it is a quantity then there is no finite formula for it. If it is the output of a formula then it is something that converges on the quantity but never reaches it.
Arithmetic is broken. Modular arithmetic is ok though.
"The square root of two" is a way to describe a formula. The formula is a construction that generates outputs. The outputs differ depending on how many iterations you run.
There is no "converging" on a quantity. The outputs just gain decimals.
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