I know there are proofs on this but I’m not great at math, can someone dumb it down for me?
In: Mathematics
On a more ‘philosophical’ level, it’s important to remember that there’s a difference between numbers, and our *representations* of numbers.
There’s only one “one” in the abstract sense, but we can represent it in numerous different ways. We can write “one”, or use the roman numeral I, or we can use digits. But even using digits, we don’t have a unique representation. We can write “1”, but we can also write “1.0”, or “1.000”.
It’s also the case that our representations don’t perfectly cover every case. It is literally impossible to write out 1/3 using only decimal digits; we need to “cheat” but putting a line over some of the threes to indicate an infinitely repeating decimal. But critically, this isn’t something intrinsic to “1/3”; rather, it’s a consequence of our base 10 number system. If we used a base 12 number system, with the digits [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, a, b], then we could write 1/3 as 0.4. No repeating decimal!
So all the math proofs here are 100% correct, but if there’s still a part of your brain that needs to say “but look how it’s written, it’s clearly a different number!”, remember that the digits are a different thing from the concept, and that the way we write things means that sometimes things look odd. Just like 2/3 is 0.66666…, and manages to be 2/3 despite it seeming like adding ever more 6s will never quite be enough to get there, 0.99999… manages to be 1. Because you’re not just “adding more 9s” – there’s an *infinite number of 9s.* And infinities are hard to write, and hard to conceptualize.
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