- #1
Danijel
- 43
- 1
So, I know that the inequality √f(x)<g(x) is equivalent to f(x)≥0 ∧ g(x)> 0 ∧ f(x)<(g(x))^2. However, why does g(x) have to be greater and not greater or equal to zero? Is it because for some x, f(x) = g(x)=0, and then > wouldn't hold? Doesn't f(x)<(g(x))^2 make sure that f(x) will not be equal to g(x)?
If that is so, then how is now √f(x) < g(x) equivalent to f(x)≥0 ∧ g(x)≥0 ∧ f(x)>(g(x))^2, where g(x) can now be equal to zero?
Also, what happens to the conditions when √f(x)≤g(x) or √f(x)≥g(x)?
If that is so, then how is now √f(x) < g(x) equivalent to f(x)≥0 ∧ g(x)≥0 ∧ f(x)>(g(x))^2, where g(x) can now be equal to zero?
Also, what happens to the conditions when √f(x)≤g(x) or √f(x)≥g(x)?