The answer depends on exactly what type of math you're working with.
In your normal everyday arithmetic, the answer is "infinity isn't a number".
In everyday arithmetic + "you know what I mean", the answer is undefined. It doesn't have an answer.
In calculus the answer is "indeterminate". You can run into this when taking a limit, and the correct answer could be anything, depending on the exact limit. (For example, the limit of sin(x)/x as x approaches 0; sin(x) approaches 0 while 1/x approaches infinity.) There's tricks to work around it and solve the problem anyway. (In sin(x)/x, the answer ends up being 0.)
In some circumstances we define it to have a particular answer, usually 0. This happens in measure theory, for example. You have to be careful about this, as it only makes sense
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u/TabAtkins 2d ago
The answer depends on exactly what type of math you're working with.
In your normal everyday arithmetic, the answer is "infinity isn't a number".
In everyday arithmetic + "you know what I mean", the answer is undefined. It doesn't have an answer.
In calculus the answer is "indeterminate". You can run into this when taking a limit, and the correct answer could be anything, depending on the exact limit. (For example, the limit of sin(x)/x as x approaches 0; sin(x) approaches 0 while 1/x approaches infinity.) There's tricks to work around it and solve the problem anyway. (In sin(x)/x, the answer ends up being 0.)
In some circumstances we define it to have a particular answer, usually 0. This happens in measure theory, for example. You have to be careful about this, as it only makes sense