Infinite- Infinitesimal Combinations

What is Infinity - 1/infinity

What is infinity i+1/infinity?

And so on...

Nope. The 2 equations cannot be broken down any further.

Such as is true of 1+(1/infinity)

Not just "Infinity" but "Infinity+."

Infinity - 1/infinity = lim x→∞ [ x ] - lim x→∞ [ 1/x ] = ∞ - 0 = ∞

infinity i + 1/infinity =  lim x→∞ [ xi ] - lim x→∞ [1/x] = ∞i + 0 = ∞i (it already in a simple form and cannot be reduced any further)

(1/infinity)^-1=infinity/1

While

(-1/infinity)^-1=-infinity/1

Showing they are separate.

That interesting, I still believe in the limit proof method and this is what I found.

(1/infinity)^-1 = 1 / (lim x→∞ [ 1/x ]) = 1/0 = undefined

(-1/infinity)^-1 = 1 / (lim x→∞ [ -1/x ]) = 1/0 = undefined

This is probably because 1/infinity = -1/infinity = 0  and  0^-1 = 1/0 still undefined. But your method of proof doesn't seem to be wrong either.

As x approaches 0, then 1/x will approach +/infinity,

Which 1/0 is.

My proof shows the "2" Infinities differ.

Nope 0^-1 equals "1/0" Which is Positive and Negative Infinity, AS a limit.

While ♾️^-1 equals only +♾️

What is the value of (-1)^∞ , i^∞