∞ - 2(∞/2)
There are more advanced questions on here but I often get caught up on nuances in the "basics".
It seems important to clear these things up before moving on.
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6Since $\infty$ is not a number. – Dr. Sonnhard Graubner Jul 16 '19 at 17:37
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2Perhaps, it would help to know what type of arithmetic is allowed if you choose to work with infinity in your number system: https://en.wikipedia.org/wiki/Extended_real_number_line#Order_and_topological_properties – cmk Jul 16 '19 at 17:41
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See https://math.stackexchange.com/questions/3102813/is-infty-undefined/3102868#3102868. – Michael Hoppe Jul 16 '19 at 17:47
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Possible duplicate of What is the result of $\infty - \infty$? – Lee David Chung Lin Jul 17 '19 at 02:51
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You're trying to evaluate $\infty-\infty$. This is an indeterminate form, one of several operations using $+,\,-,\,\times,\,\div$ on two extended real numbers (of which $\infty$ is an example) that can't be defined. In particular, functions $f,\,g$ can satisfy $\lim_{x\to0}f(x)=\lim_{x\to0}g(x)=\infty$ with just about any behaviour for $\lim_{x\to0}(f(x)-g(x))$. You can get $\infty$ from $f=\frac{2}{x^2},\,g=\frac{1}{x^2}$, $-\infty$ if you exchange these, $0$ if you use either function twice, your favourite real number if you then add it to $f$, or none of these behaviours if you add $\sin x$ to $f$ instead.
J.G.
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