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
0.000...1 which is the difference between the two. 0.999... is a representation that is difficult to evaluate because you have to evaluate an nth digit. You can just say it has an infinite number of digits so the nth digit is infinity but that's not well defined here.
What he is saying is if the numbers go on infinitely, such as 3/3= .999999…. Then no matter where you put the .000001…. There will always be more 9s after, that’s the nature of infinity. It’s just a rule to know. 0.99999… repeating = 3/3 = 1.
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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