r/askmath • u/Loose-Balance3225 • May 06 '26

Discrete Math Can infinity contain infinity

If pi has no end it has to have every combination of numbers but could it hold an infinite combination? Like 1 2 3 4... To infinity

Please help this is missing my brain up

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u/ButterSlicerSeven May 06 '26

Yes. Here's a 7th grade maths proof.

Take the natural numbers: 1, 2, 3 ... and so on to infinity. The set of natural numbers is infinite. Now take integers: ... -3, -2, -1, 0, 1, 2 ... and so on to infinity. It's clear that the set of integers includes the set of natural numbers. Thus, infinity can contain infinity.

Alternatively, we can take a geometric approach: take a straight line. Straight line goes to infinity in two directions. Now divide it in 2, the two resulting halves will go to infinity in opposite directions.

As per Pi, this is not really a related concept. What you want to know is whether Pi is a normal number or not, which we do not know for certain. It might be, or it might be not, we have no clue.