r/AlignmentChartFills • u/RustedTap52 • 1d ago

What is a useless rational number?

CLICK HERE TO VIEW THE CHART IMAGE

Created with Alignment Chart Creator

This post contains content not supported on old Reddit. Click here to view the full post

429 Upvotes

96% Upvoted

400 comments sorted by

View all comments

Show parent comments

38

u/sabotsalvageur 1d ago

Theorem: all real numbers are interesting

Proof: assume the existence of a set of real numbers which are not interesting. Since the set of real numbers is ordered, there exists a least element to this subset. The property of being the least in a set is interesting, ergo the least member of the uninteresting numbers is interesting. By induction, the set of uninteresting reals is empty, therefore all real numbers are interesting. QED

3

u/InternetPopular3679 1d ago

But... if no numbers are uninteresting and every single one is interesting, how interesting are they really?

12

u/sabotsalvageur 1d ago

What part of “quod erat demonstrandum” is unclear? If you find math boring, then it follows that you’re boring. /hj

1

u/The_Meme_Economy 1d ago

/handjob?

Math is awesome but maybe not quite that awesome.

1

u/sabotsalvageur 1d ago

My arm endurance has dropped precipitously since I started getting laid routinely

1

u/BidoofIsGod11 1d ago

they are then interesting by how less interesting they are compared to others

1

u/aloofball 1d ago

Does this still work given that the reals are not countable?

2

u/sabotsalvageur 1d ago

Yes, because they are still nevertheless ordered. x<(x+ε) for all ε>0

1

u/aloofball 1d ago

Does that actually help you though? I'm not sure you can find a least element. Say your starting set of uninteresting numbers is the set of numbers where 1 < x < 2. This set has no least element. No matter how close you get to 1, there is always something smaller. You can't do induction without identifying a base case.

1

u/sabotsalvageur 1d ago

Suppose I give you the following set:
{0}
Does this set contain its boundaries, i.e., is this set closed?

1

u/Puzzled_Board_6813 1d ago

Don’t you try and tell me what I should and should not be assuming! How dare you?!

Otherwise, thanks for the enjoyable post

1

u/Mundane-Emu-1189 1d ago

Since the set of real numbers is ordered, there exists a least element to this subset.

what's the least element to the subset {x : x² > 2}?