-(infinity)^5 + infinity - 1 = -infinity + infinity (is it now positive or negative infinity?)
You can't add infinities...infinity is not a number. But we can still do a comparison. Which is bigger for large numbers (not infinite ones), $\displaystyle x^5$ or x?
You can't add infinities...infinity is not a number. But we can still do a comparison. Which is bigger for large numbers (not infinite ones), $\displaystyle x^5$ or x?
Better is to write $\displaystyle -x^5+x = x(1-x^4) \to \infty \cdot (-\infty) = -\infty$
Or $\displaystyle -x^5+x > -x^5$ (where $\displaystyle x > 0$).