Viewing a single comment thread. View all comments

M8dude t1_j29dbmx wrote

Reply to comment by alukyane in There’s just as many numbers between 0 and 1 as there is from 0 to infinity. by Resinate1

well said, although it should be the bijection 1/(x+1) for OP's claim, but that's me nitpicking.

also i think it's natural to assume that OP is talking about the real numbers and the 'counting measure'.

3

jaydfox t1_j29ejxx wrote

I think they meant (1/x)-1, not 1/(x-1)

4

M8dude t1_j29f874 wrote

aaaah (1/x)-1 is the inverse of 1/(x+1), i mixed up the sets and thought there'd be a mistake, my bad.

6

alukyane t1_j29eswo wrote

(1/x)-1 is correct for going from (0,1) to (0,infty).

Your function would send the interval (0,1) to (1/2,1) in a weird reversed/distorted way (check endpoints to confirm).

And the op is most likely talking about cardinalities, not the counting measure, if we're nitpicking. :)

3

M8dude t1_j29ftq5 wrote

yes, you're right, my mistake, but to justify, (1/x)-1 is the inverse of 1/(x+1), so there we are :P

1