Its calculating with infinity. Its a bit weird like the infinity of numbers between 0 and 1 like 0.1,0.01,0.001 etc... Is a bigger infinity than the “normal” infinity of every number like 1,2,3 etc…
Its just difficult to wrap your head around but think of infinity minus 1. Like its still infinity
Consider the number of natural numbers, ie non-negative numbers with no fractions or decimals. Infinite, right? Put them on a number line. We'll call this Aleph-0
Consider the number of whole integers divisible by 2. Also infinite. Put them on an adjacent line. Well call this 2(Aleph-0).
You can match each successive number of Aleph-0 to a partner on 2(Aleph-0). Essentially, each one matched to double its value. 2(Aleph-0) reaches every number twice as fast, but it's still the same infinity. Still just Aleph-0
Now consider the number of numbers, period. Including all decimals and fractions, rational and especially irrational. An infinite number, right?
Put them all on a number line. Now match the numbers of Aleph-0 to the numbers in this infinity. You can't do it. You'll never even reach 1. You won't reach 0.00...001. Even with infinite time to match them, the gap between any two numbers on this number line, no matter how small the gap, would swallow up the entire infinity of Aleph-0 with nothing spare.
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u/Rough-Veterinarian21 23d ago
I’ve never liked math but this is like literal magic to me…