Since the limit of ln(x) is negative infinity, we cannot use the Multiplication Limit Law to find this limit. At first, you may think that infinity subtracted from infinity is equal to zero. This is the definition of undefined. Another way of looking at this is that no one can EVER finish multiplying zero times infinity, therefore the answer will always be undefined. If any number times zero is zero and any number time infinity is infinity, then what do you get when you multiply zero times infinity? "also can 0 and infinity be one an others inverse? So, zero times infinity is an undefined real number. We are assuming ∞ ∞ \frac{\infty}{\infty} ∞ ∞ is defined, which has been disproven using a similar technique used in the problem. New content will be added above the current area of focus upon selection What does Infinity Minus Infinity Equal? Reply: You are dividing by infinity, which is not legal here. Do they cancel one another out and equal any number since any number = 0 to infinity) and any number infinity to 0? Infinity Times Zero Return to the Limits and l'Hôpital's Rule starting page. Rebuttal: If ∞ × 0 ≠ 0 \infty \times 0 \neq 0 ∞ × 0 = 0, then 0 ≠ 0 0\neq 0 0 = 0. I am going to prove what infinity minus infinity really equals, and I think you will be surprised by the answer. Therefore, zero times infinity is undefined. We can convert the product ln(x)*sin(x) into a fraction: . After all, any number subtracted by itself is equal to zero, however infinity is not a real (rational) number. In this case, there is no fraction in the limit. Consider .