Question

Anbody, who can explain "Big O notation"?
(Its a language for controlling growth)

Answer 1

Check attachment for more details..
Please explain me someone.....

Answer 2

I think this will help you https://en.wikipedia.org/wiki/Big_O_notation

Answer 3

@Astrophysics
Its so hard to understand....
but its interesting... it proves What is Differentiation in a totally new way...

Answer 4

I've seen it written in some papers...I was like what is this? when I read them

Answer 5

If I understand, I will give in Informative.

Answer 6

@Empty

Answer 7

@phi please explain in terms of some functions like factorial, exponential, polynomial..

Answer 8

Is it Factorial>Exponential >Polynomial>Logarithmic>Constant.

Something like this @phi

Answer 9

Is that the reason we use logarithmic functions in s=k logw ( Chemistry)...
To calculate in terms of small numbers....

What about factorial? where is it used then? and why?
@phi

Answer 10

is that MATH104? With Ghrist?

Answer 11

Yes Yes..... @UnkleRhaukus

Answer 12

it does not explain differentiation in a different way. It characterizes your function and that's the basic thing it does.

Answer 13

okay...@nincompoop , characterise in the sense?

Answer 14

Big Omicron notation is used to describe how a function behaves as the input becomes very large, or very small.
The ‘O’, stands for Order of growth.

f(x) = 5 + 2x

is said to be of ‘linear order’ as x increases, which we can write as
f(x) is O(x), [if x was hundreds , f(x) would be hundreds ]


just as
g(x) = 5 - 2x + 20x^2
is said to be of ‘quadratic order’ (with increasing x)
g(x) is O(x^2) [if x was thousands , g(x) would be millions]

_

Basically only the dominant term appears in the expression for the order of growth.
_

If instead we consider x to be decreasing towards zero:

f(x) = 5 + 2x

is now said to be of constant order; O(1), the 5 is now the dominant term
[if x was a few percents, f(x) would be of constant order (still about 5) ]

and
g(x) = 5 - 2x + 20x^2
would, likewise be of constant order as x decreases (to zero)

Answer 15

Awesome Explanation @UnkleRhaukus
Thumbs up....!

Answer 16

characterizes your function as changes occur (if your value of x, y, or z grows bigger or smaller)

Answer 17

Anyway thank you @nincompoop
I understood..
Thank you so much... @UnkleRhaukus

Answer 18

This is probably a good way to see some statistical analysis such as when the curve is not normalized (difficult to analyze with high degree of certainty) and by increasing the number of sample, it goes towards normalization over time, but with ever decreasing deviation and ever increasing steepness of curve.