Well, there’s non-standard analysis, where you actually have infinite and infinitesimal numbers, and there’s casual talk of infinite limits, but the latter need not involve the former. Normally it’s just a shorthand for the epsilon-delta type of argument that was worked out in the 19th century.
I have plenty of times heard of variables being infinitive in physics and I have seen people do calculus with infinitvely small numbers.
Well, there’s non-standard analysis, where you actually have infinite and infinitesimal numbers, and there’s casual talk of infinite limits, but the latter need not involve the former. Normally it’s just a shorthand for the epsilon-delta type of argument that was worked out in the 19th century.