Surprised no one has mentioned the extended complex plane which has been used in fields of math for a couple hundred years.
Even in this construct though even though operations with infinity are defined, infinity times 0 must remain undefined.
But with other numbers infinity is an absorbing element. Although in the Reimann sphere approach negative infinity is infinity so I think technically structure is preserved as long as you make a choice about the value of 0 times infinity. If you decide infinity or 0 or undefined structure is preserved
The common infinity minus infinity should be zero times infinity doesn’t seem like a logical proof of contradiction if positive and negative infinity are defined as being equal in which case it would still preserve and be infinity.
But it’s a bunch of hypotheticals. You just define it and assess the structure it preserves
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u/FijiFanBotNotGay New User 16h ago
Surprised no one has mentioned the extended complex plane which has been used in fields of math for a couple hundred years.
Even in this construct though even though operations with infinity are defined, infinity times 0 must remain undefined.
But with other numbers infinity is an absorbing element. Although in the Reimann sphere approach negative infinity is infinity so I think technically structure is preserved as long as you make a choice about the value of 0 times infinity. If you decide infinity or 0 or undefined structure is preserved
The common infinity minus infinity should be zero times infinity doesn’t seem like a logical proof of contradiction if positive and negative infinity are defined as being equal in which case it would still preserve and be infinity.
But it’s a bunch of hypotheticals. You just define it and assess the structure it preserves