# Arrange the functions in a list so that each function is big-O of the next function.

If 2 functions each big $$\mathcal O$$ of each other, then place them on the same level. $$x^2 + x^3, 3^x, x!, x \log(x), x^2 + 2^x, 2^{x \log(x)}, \log(x^2), 6 \log(x), 2^x, x(1+2+\dots+x)$$

$$x(1+2+· · ·+x) = x(x(x+1))/2 = x(x^2+x)/2 = (x^3+x^2)/2$$

The list is:

$$x^2+x^3, \mathcal O((x^3+x^2)/2)$$

$$3^x, 2^x$$

$$x \log(x), \mathcal O(2^{x \log(x)})$$

$$6 \log(x), \log(x^2) = 2 \log x$$

$$x^2 + 2^x$$

$$x!$$

Is this correct? Do I need to mention $$\mathcal O(....)$$ in my answer or can I remove the $$\mathcal O$$?

• Please use MathJax it hurts my eyes – Peter Foreman Apr 21 at 22:55
• Is there supposed to be a comma between $x!$ and $x\log(x)$ in your list? – Neil A. Apr 22 at 2:39
• yes..................... – ionics Apr 22 at 2:52