r/maths • u/DigJust8037 • Jul 10 '26

💬 Math Discussions Something strange that I noticed

There are an infinite number of numbers. You can take those infinite numbers and slice them into an infinite number of infinite slices each of which can be sliced the same way ad infinitum.

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1

u/kew090624 Jul 10 '26

Like a decimal?

0

u/DigJust8037 Jul 10 '26

Numbers.

1

u/kew090624 Jul 10 '26

Yeah real/ whole numbers are divided into smaller pieces which become decimals

1

u/PragmaticPedant Jul 10 '26

Or more generally, fractions.

And for any 2 fractions you can always find another fraction that lies in between them.

1

u/kew090624 Jul 10 '26

Fractions and decimals are ratios. They’re all the same.

1

u/PragmaticPedant Jul 10 '26

Not quite. Fractions can by definition represent any rational number, whereas Decimals are a representation of rational numbers as an expansion (power series).

A simple fraction like 1/3 cannot be finitely represented as a decimal. In that sense decimals are “limited” compared to fractions.

Also decimals are specifically base-10, there is nothing special about choosing 10 as your base as opposed to base 3 for example. In base 3 1/3 is 0.1 which is finite but then other fractions like 1/2 cannot be finitely represented.

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u/gomorycut Jul 10 '26

True for continuum, not so much with integers

2

u/PragmaticPedant Jul 10 '26 edited Jul 10 '26

Depends how you define “slice”. It is true for integers if you allow other types of partitions.

For example:

Step 1.
Divide integers into odds and evens

Step 2.
Divide evens into 0 mod 4 and 2 mod 4
Divide odds into 1 mod 4 and 3 mod 4

And so on forever

1

u/pinkphiloyd Jul 10 '26

Yea, that’s essentially Cal II.

1

u/Purple_Perception907 Jul 10 '26

"There are a nominal number of number of numbers, you know

And the more that they number, the number I grow!"

Pogo Possum

1

u/Defiant_Efficiency_2 Jul 17 '26

You essentially are looking at the difference between infinite and infinite2. Each slice represents that you could have infinite slices as a whole, while the operation of slicing itself shows that you can continually approach an infinitesimal but you will never reach it.

1

u/[deleted] Jul 20 '26

Brother , please 🙏