infinity maths

[suyogya]

I found most of the webpages saying infinity minus infinity is undetermined.
If infinity is not a number, then infinity minus infinity should be undefined and not undetermined because subtraction operation requires only numbers in its domain. After all there is a great difference between undetermined and undefined.

 

[tkhunny]

Most of the problem, there, is in the understanding of "infinity".
Very often, if you read it "something that increases without bound," it makes a lot more sense.
Websites in particular, are socially required to write something that will get and keep your attention. This can lead to some awkward conclusions.

 

[Dr.Peterson]

It's partly a matter of context.

As an expression in ordinary arithmetic, ∞-∞ is undefined, because ∞ is not a real number, as you say. You can't really even ask the question in that context!

As a form in discussing limits, it is called an indeterminate form, because the limit of f-g, where both f and g approach ∞ may approach any number (or none).

In extended arithmetic, where ∞ is allowed as a number, ∞-∞ is undefined because it is indeterminate! (The same is true of 0/0.)

Some sources fail to distinguish contexts, which confuses things.