- #1

n_kelthuzad

- 26

- 0

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if there exists a number ∞, than the number must equal to it self.

so "∞ = ∞" ( this and all the following are one-sided equations)

if ∞ has a 'logical maximum value' of a, than ∞=a

however, a is bigger than any other numbers in this plane. Then (a+1) must have the same properties as a.

so ∞ also equal to (a+1)

however if a=a+1, 0=1. such a number does not exist.

or for ∞/∞ [itex]\neq[/itex] 1:

a+1/a > 1 and a/a+1 < 1.

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so the number ∞/∞ (or all the other primary calculations of ∞, and 0/0) must be 'any real number' and also 'not a fixed number'. this leads me to the thinking of a higher dimension of the numeral system. Is there any way other than limits that can describe different ∞'s?

You cannot put ordinary logic into ∞, since the concept or property of infinity is:

A NUMBER THAT CAN NEVER BE PHYSICALLY REACHED.

however when I look some series:

e.g. the harmonic series 1+1/2+1/3...

and the "harmonic + 1" series that I just made up in mind

2+3/2+4/3+...

both series diverge into ∞.

however, the 2nd series is bigger than the first one, in n terms, the difference is (1n).

Does this provide a way to compare infinitys as the difference between series in a finite number of terms?

Thanks

Victor Lu, 16

BHS, CHCH, NZ