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I know that $\infty/\infty$ is not generally defined Multiplying 0 by infinity is the equivalent of 0/0 which. However, if we have 2 equal infinities divided by each other, would it be 1
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Similarly, the reals and the complex numbers each exclude infinity, so arithmetic isn't defined for it Multiplying 0 by infinity is the equivalent of 0/0. Infinity refers to something without any limit, and is a concept relevant in a number of fields, predominantly mathematics and physics
The english word infinity derives from latin.
Can this interpretation (subtract one infinity from another infinite quantity, that is twice large as the previous infinity) help us with things like limn→∞(1 + x/n)n, lim n → ∞ (1 + x /. In the process of investigating a limit, we know that both the numerator and denominator are going to infinity. But we dont know the behaviour of each dynamics I understand that there are different types of infinity
One can (even intuitively) understand that the infinity of the reals is different from the infinity of the natural numbers Infinity times zero or zero times infinity is a battle of two giants Zero is so small that it makes everyone vanish, but infinite is so huge that it makes everyone infinite after multiplication This resolves your problem because it shows that 1 ϵ 1 ϵ will be positive infinity or infinite infinity depending on the sign of the original infinitesimal, while division by zero is still undefined
The infinity can somehow branch in a peculiar way, but i will not go any deeper here
This is just to show that you can consider far more exotic infinities if you want to Because multiplying by infinity is the equivalent of dividing by 0 When you allow things like that in proofs you end up with nonsense like 1 = 0
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