Pretty sure this is proven to be, āindeterminateā for the same reason x/0 is.
Specifically under: properties: cardinality
We can argue that the amount of numbers between 0 and 1 is āAā
(also this will be in base 10 so an answer can be derived, but base 10 is arbitrary and a different base with equal viability will give a different answer, ergo indeterminacy)
And amount of numbers between 1 and something is āBā
A={0,0.1,0.2,0.3ā¦0.9,1.0}
B={1.0,2.0,3.0ā¦9.0,10.0}
Now B{[1.0,2.0]} contains all of A.
B/100={.01,.02,.03ā¦.09,0.10}
Now the magnitude of a set should not impacted its length:
āIf I have 10 items, but they now have a different size, how many items do I have?ā
But B/100 is now contained by A{[0.0,0.1]}
We can establish B= an infinite set which contains goes from n=0 to n=set_index of :
10^-(Ceil(set_index+epsilon)/10) ā¢each number of Bās. infinite set based on n
Where the above has equal length to the set at hand and when multiplied by the 10^ (Ceil(highest possible set index + epsilon)/10) the originally B set will be scene in this magnification.
When we have B zoomed out like this, B becomes a subset of A
.This is arbitrarily recursive, for you could throw this zoomed out B set to be arbitrarily smaller or larger depending on modular system, and arbitrarily smaller or larger than the A set, which means you could choose by what difference any given B set is larger than any given A set (negative meaning smaller than).
This can be done because you are treating infinity like a number rather than a rate, which is why calculus works, but this doesnāt.
Note: these problems arise even if we donāt have Bās upper bound being infinity, and because youāve merely said infinity, and itās undefined in 2 ways that do not cancel eachother out.
So the correct answer is:
āThatās scaryā¦ I donāt knowā¦.ā!!!
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