How do we prove that an equation maps to Big o of something?

[wet bronze]

Hello, can someone explain how do we prove that an equation is an element of big O of something pls.

For e.g., how do we prove the equation in the picture pls.

In the mathematical definition we talk about a constant and n naught. Can someone explain what it is and where it is used pls

[grave sluice]

weird, since the n term is linear its growth rate cant be quadratic unless im missing something

[wet bronze]

I'm confused because in the video the user rewrite the equation as:

2n + 3 <= 2n^2 + 3n^2

How did we obtain the 2n^2 + 3n^2 ?

[grave sluice]

Oh

It just means 2n^2 + 3n^2 grows faster than 2n+3 for sufficiently large n

Which is like true

But 2n+3n also grows faster than 2n+3

[wet bronze]

https://www.youtube.com/watch?v=0asZleBjer0

This is the video I'm watching

I'm confused when the user start explaining with the examples, like I don't understand how we obtain these equations, there are no cues

[grave sluice]

g(n) is just chosen so that for large enough n it outgrows f(n)

Frfr

It like is kinda arbitrary

[wet bronze]

hmmm

ok, will read a bit and come back if I have other questions, thanks !

.solved