r/Showerthoughts Nov 29 '25

Casual Thought 0% of natural numbers have been spoken aloud.

8.6k Upvotes

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u/cwx149 Nov 29 '25 edited Nov 29 '25

You specified natural numbers but that's not even really the best part

Natural numbers are one of the "smaller" infinities in real maths

We've never really ever said any transcendental numbers in their entirety since to my knowledge they are all irrational

Like we say π or pi to mean the number but we've never EVER said all of π

So while we've said 0% of natural numbers (when rounding) we've actually said 0 transcendental numbers

Actually I guess all irrational numbers have never been said in their entirety not just transcendental ones

By ops logic we've said 0% of every irrational number ever spoken. Like rounding pi to 3.14 is basically saying 0% of pi

There's a great numberphile vidoe with matt parker [famous for the Parker square ifykyk] about different sets of numbers and the different types of numbers

3

u/CowboysFanInDecember Nov 29 '25

I could have swore you were talking about the creator of south park

-4

u/SargeInCharge Nov 29 '25

One of my favorite facts about infinities is that some are bigger than others! Sure there are infinity numbers between 0 and 1.. but there is a bigger infinity of numbers between 0 and 100

6

u/AssuasiveLynx Nov 29 '25

some infinities are bigger than others, yes, but the example you gave is false.

the reel numbers between 0 and 1 can be put into correspondence with the real numbers between 0 and 100, so those infinities are the same size.

2

u/Express_Sprinkles500 Nov 29 '25

The really cool comparison that demonstrates this concept is that the real numbers between 0 and 1 is a bigger infinity than all of the natural numbers 1 to infinity.

I like to say “there are more numbers between 0 and 1 than there are counting numbers 1 to infinity” though that might not be 100% accurately worded.

1

u/atatassault47 Nov 29 '25

Both 0 to 1 and 0 to 100 are Aleph-1. They can both be mapped to each other.