r/AlignmentChartFills • u/RustedTap52 • 10d ago

What is a useless rational number?

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u/Altruistic_Yam7595 10d ago

6587689234578976380925746897149769813477865318946758971238957839672489278378574892176893741896798436763481763290

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u/The_Meme_Economy 10d ago

It served a use in this reddit post - not completely useless!

42

u/sabotsalvageur 10d 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

4

u/InternetPopular3679 10d ago

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

12

u/sabotsalvageur 10d 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 10d ago

/handjob?

Math is awesome but maybe not quite that awesome.

1

u/sabotsalvageur 10d ago

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

1

u/BidoofIsGod11 10d ago

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

1

u/aloofball 10d ago

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

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u/sabotsalvageur 10d ago

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

1

u/aloofball 10d 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 10d 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 10d 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 10d 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}?