a thing that i think mathematicians and physicists don’t do a good job of conveying is that most of our use of large infinite objects like the real numbers is a matter of convenience. the infinite is a convenient approximation of the merely unimaginably large finite
Conversation
wait
2
11
this is not a universal opinion to be clear but i think it’s quite defensible. doron zeilberger is notably very vocal about this: users.uoa.gr/~apgiannop/zei
2
24
well fuck
1
12
lol sorry was this load-bearing i am happy to talk more
3
2
17
Is that related to this being true?
0.999... = 1
2
3
that's because repeating numbers give inexact solns. 1/3 *3 = 1, but 0.333(repeating) *3=0.999, so 0.999=1. we face this issue in binary too. 0.1 and 0.2 are repeating decimals in binary, so although in decimal they add up to 0.3, any prog lang will eval 0.1+0.2 as sth close to
1
1
but not exactly 0.3. But this is a problem with our representation of numbers in a chosen base, not the numbers itself. 0.1+0.2=0.3 and 0.333 (repeating) *3=1
what qc's talking about is infinite series. zeno says you have to cover 1/2 then 1/4 then 1/8 etc forever,
1
1
which is impossible, but the series 1/2+1/4+1/8+...=1, so you get a finite sum from an infinite series.
1
1
qc, are these two related?
1
1
repeating decimals are infinite series! saying that 1/2 + 1/4 + 1/8 + ... = 1 is the same as saying that in base 2, 0.111... = 1