Depends what you mean by infinity. If you're working in the extended real numbers, which is just all the regular numbers plus a +infinity that's greater than all of them and a -infinity that's less than all of them, then +infinity + 1 = +infinity, but +infinity - +infinity is undefined, not 0.
Meaning (infinity +1) - infinity is also undefined.
Depends what you mean by infinity. If you're working in the extended real numbers, which is just all the regular numbers plus a +infinity that's greater than all of them and a -infinity that's less than all of them, then +infinity + 1 = +infinity, but +infinity - +infinity is undefined, not 0.
Meaning (infinity +1) - infinity is also undefined.