Stupid Question Thread /SQT/

Okay will do.

Is there a specific name to the formulas you provided? I'll pick up a combinatorics book either way.

the formula is P(E1 or E2)=P(E1)+P(E2)-P(E1 and E2)
with P(E1 and E2) being 0 for mutually exclusive events.

What's the point in using a taylor series? Why approximating a function if you already know it?

For calculating shit.
Also, you don't always know it.

Google perturbation theory.
Also, almost everything in physics is based off of a Taylor expansion.

"Everything is harmonic on the second order."

How did you go about deriving this? This works for this particular problem. Would it work on general for such a problem? Thank you so much!

Alright my man what is the sin of 3 to 3 decimal places?

Taylor series are also incredibly useful for more theoretic purposes. Approximations need to be made in physics and numerical analysis, and Taylor series are usually the way to go.

Define an operation * as following:

1)a*b is defined for every ordered pair (a,b)
2)a*b must be uniquely defined
3) a*b must be closed

#1:

is a*b = |a-b| on the set {n in Z: n>=0} an operation?

I know |a-b| has two solutions

x=a-b and x= -a + -b

so due to that is it correct to say that |a-b| is not an operation?

#2:

Is a*b = sqrt(|ab|) on the set Q an operation?

How do I go about solving this?

I NEED STUDY METHODS

GIVE ME STUDY METHODS

No really though I want to spend some time studying before starting my Master's program in late August but I genuinely have no knowledge of efficient study methods, how-to, so on and so forth. I'll accept literally any suggestions.