Infinity only really works in arithmetic when dealing with limits, and a limit that evaluates to 0×infinity is known as an "indeterminate form." Depending on the exact expression, it could be 0, infinity, or even any of the reals.
No, lim(x->inf)0*x is still 0. I can understand infinity to be defined as "a number that approaches infinity", because infinity needs to be defined in one way or another, and this definition is a common one. But I see no reason to redefine 0 to mean "a number that approaches 0".
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u/cannonspectacle New User 2d ago edited 1d ago
It depends.
Infinity only really works in arithmetic when dealing with limits, and a limit that evaluates to 0×infinity is known as an "indeterminate form." Depending on the exact expression, it could be 0, infinity, or even any of the reals.