Week 6: Cases, multiple quantifiers, limits

Proof about non-boolean functions
Boolean function - a function whose return value is True/False - example x>5
Non-boolean function - not a function of such as above - example x^2
Floor for x - the largest integer that <= x
Steps to proof one is correct
1) fully understand the definition
2) breaks the definition into predicates
3) play around with those predicates
4) proof!

Proof something false
To disprove a statement S, just proove NOT S
1) negate the statement properly
2) prove the negation

Proof by puns (SERIOUS PROOF)
A cow have four more legs than no cow.
No cow has five legs.
Therefore, a cow has nine legs.

Proof by intimidation (ALSO VERY SERIOUS TECHNIQUE)
Trivial!!!!!
or
Don't be STUPID, of course it's true!

Proof by intuition (WHO DOESN'T)
I have a dre... I mean I believe....!

Proof by clever variable choice (BE SMART ABOUT IT)
Let A be the number such that this proof works...

Proof by hasty generalization (WELL IF IT WORKS IT WORKS)
Well, it works for 17, soooo~

Proof by tautology/begging the question (FOR ALL THE BELIEVERS)
God exist because the BIBLE said so!

Proof by convenience
It would be nice if it were true, so.....

Proof by beautiful typesetting (...Yea)
Because the proof looks good and is typed in LaTex...

Proof by *%^*% (Can't read)
I^$#%&*^$&^#

Proof about limits
OK I am done with limits, so they are like out of my limit...
but I will say this
Wise choices are often found by backward search
DON"T freak out unnecessarily!