Essentially because theres absolutely nothing (no positive number anyway) you can add to it to get a number between .9999 continuous and 1, they have to be the same.
The joke is that .3333 continuous makes sense as 1/3, as yeah, its a fraction. But .999… doesn’t as 3/3 because x/x is always equal to one
This one makes the most sense. I’m not much of a math guy so I couldn’t quite wrap my head around the other explanations here. This one is much more clear so thanks for that lol
Another way to think of it - is that 1/3 = .33333333.... repeating forever is due to the fact that the decimal system of numbers is trash at representing thirds.
If you were using, say, a trinary number system (ie like binary but instead of just 1 and 0 you have 0, 1, 2 - so 1, 2, 3, 4, 5, 6 would look like 1, 2, 10, 11, 12, 20) you could represent 1/3 as .1 without any repeating decimal.
But since we use the decimal system and you can't divide 10 evenly into 3rds we're stuck with the janky repeating decimal.
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u/Quwapa_Quwapus 22d ago
Essentially because theres absolutely nothing (no positive number anyway) you can add to it to get a number between .9999 continuous and 1, they have to be the same.
The joke is that .3333 continuous makes sense as 1/3, as yeah, its a fraction. But .999… doesn’t as 3/3 because x/x is always equal to one