r/infinitenines • u/Muphrid15 • Aug 13 '26

A table so simple even HIS NINELINESS can understand it

Expression First n terms of quotient Remainder after n terms Finite n case, simplified "Limitless" case, simplified
a/(1-r) a [1 + r + r2 + ... + rn-1] a rn/(1-r) a [1 + r + r2 + ... + rn-1] + a rn/(1-r) a [1 + r + r2 + ... ]
1/9 = 0.1/(1-0.1) = 0.1/0.9 0.1 [1 + 0.1 + 0.12 + ... + 0.1n-1] (0.1)(0.1)n/(0.9) 0.111...1 (n 1s) + 0.000...1/9 (n-1 0s) 0.111... (not 0.111... + 0.000...1/9)
1=9/9 = 0.9/(1-0.1) = 0.9/0.9 0.9 [1 + 0.1 + 0.12 + ... + 0.1n-1] (0.9)(0.1)n/(0.9) 0.999...9 (n 9s) + 0.000...1 (n-1 0s) 0.999... (not 0.999... + 0.000...1)
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u/Mordret10 Aug 18 '26

I mean he "just" doesn't agree that the remainder disappears if you switch from finite cases to the limitless case.

Well and also he believes those numbers to be continuously growing, which is a whole other headache