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Person: If I start at 0 and count up in infinitesimal increments to the number one how many numbers must I count?
Wiseman: infinite
Person: and if i start at 0 and count up in infinitesimal increments an infinite number of times what number will I arrive at?
Wiseman: all of them
@freemo @math Funny enough, I don’t think this is true for hyper real infinitesimals. Certainly any finite sum of infinite reseals is infinitesimal, but I think a infinite sum of a single infinitesimal would have to jump straight to “hyper infinity,” the upper limit was n the corresponding compactification.
@mandlebro
Yea its not real in any formal math sense I know of
@math
@freemo @math To the latter question.
Wiseass: A real number because addition with imaginary numbers would result in all imaginary numbers.
A rational number because there would be three infinities being multiplied, resulting in infinity as they would be the same type of infinity. See the first question's answer for the sum that approaches but never reaches 1. Perhaps an uncountable infinity would be of great enough magnitude to handle these exceptions.
The set of all numbers generated would be missing the subsets of Imagery Numbers and Irrational Numbers.
@freemo
Zeno would like a word…
@math