We seem to agree on this: you don't think there's any need for a way to determine whether two real numbers are equal.
For ordinary math, though, using some criterion for equality (for example x>=y and y>=x) is basic and not controversial. So it seems unconvincing (to me) when you seem to imply the opposite.
There is an easy way to prove two numbers are equal. Typically in the reals there are three possibilities: a > b, a < b, a = b. If you eliminate a > b and a < b then you are left to conclude a = b. And this is exactly what is done in Apostol's Calculus Vol 1 (IMHO the greatest calc book ever written) chapter 1 when he proves that the area under n^2 is EXACTLY (n^3)/3, with no "calculus". You would be shocked how far into calculus the author gets with just that theorem. Can't recommend that book enough.
> you don't think there's any need for a way to determine whether two real numbers are equal.
You are putting words in my mouth.
And you clearly do not understand the answer.
I guess I'm not very good at ELI5 because I very clearly answered your question with your own proposal.
Maybe when you get to college a professor can do a better job explaining it to you (if you actually make it to college, because you're going to struggle very hard if that's how you think when an answer is spoon-fed to you).
tom-thistime|5 years ago
For ordinary math, though, using some criterion for equality (for example x>=y and y>=x) is basic and not controversial. So it seems unconvincing (to me) when you seem to imply the opposite.
esmi|5 years ago
0xff00ffee|5 years ago
You are putting words in my mouth.
And you clearly do not understand the answer.
I guess I'm not very good at ELI5 because I very clearly answered your question with your own proposal.
Maybe when you get to college a professor can do a better job explaining it to you (if you actually make it to college, because you're going to struggle very hard if that's how you think when an answer is spoon-fed to you).