Barry Goldman on Nostr: npub1zdp33…2vqv8 as opposed to not continous ANYWHERE it is defined, like f(x) = 0 ...
npub1zdp33shl69xr0uq3x8n5gsjykq9upycwh6nqm02c3f6x0frrn0dq42vqv8 (npub1zdp…vqv8) as opposed to not continous ANYWHERE it is defined, like
f(x) = 0 if x is rational
=1 if x is irrational
defined everywhere, continuous nowhere
for 1/x i think the point is tat if defined from R->R there is NO way to MAKE it continuous at 0
i think if you extend it to the complex numbers there is a way... i don't remember how it works.
f(x) =(x-1)/(x^2-1) CAN be defined to be continous at x=1
anyway that's how i'd look at things
f(x) = 0 if x is rational
=1 if x is irrational
defined everywhere, continuous nowhere
for 1/x i think the point is tat if defined from R->R there is NO way to MAKE it continuous at 0
i think if you extend it to the complex numbers there is a way... i don't remember how it works.
f(x) =(x-1)/(x^2-1) CAN be defined to be continous at x=1
anyway that's how i'd look at things