>>13906262Infinity is not a number.
"Definitions" like 1/(infinity) = 0 are just a mnemonic to remember how to treat certain limits.
1/(infinity) is not "undefined" in the sense that any limit that leads to that expression ALWAYS equals zero.
1^(infinity) is "undefined" in the sense that two limits may lead to that same expression and yet the limits may have different values. For example, 1^x tends to 1 when x tends to infinity, while (1 + 1/x)^x tends to e as x tends to infinity and we have e > 1 so the two limits have different values and thus 1^(infinity) is called an "indeterminate form".
0/0 is also another indeterminate form and thus the expression 0/0 is "undefined". Every derivative is a result of calculating a limit of the form 0/0, yet a derivative can literally have any value whatsoever.
