Wednesday, December 3, 2014

LaTex Copy & Paste / Assignment 3

I finally found the way to copy & paste LaTex codes.

Simply visit https://latex.codecogs.com/ this website, create a code, and copy + paste on the blogger's compose panel.

\forall e \in \mathbb{R}^+, \exists d \in \mathbb{R}^+, \forall x,y \in \mathbb{R}^+, |x-y|>d \Rightarrow |x+y|>e
This is one of the assignment-3 questions which I have to review because I still misunderstood how the order of quantifiers matters.

I thought this is false, but it's actually true.
\exists e \in \mathbb{R}^+, \forall d \in \mathbb{R}^+,\exists x,y \in \mathbb{R}^+, |x-y|>d \wedge |x+y| \leq e
When I negated the claim as above, I could pick e, x and y. I picked
e = \left \lceil d \right \rceil + 3
 and
 x = 1, y = d + 2
It works, iff the claim is:
\forall d \in \mathbb{R}^+, \exists e \in \mathbb{R}^+ ....
like this. I actually picked the variable "d" before "d" is introduced. The professor told us about the ordering of the quantifiers is significant when proving such claims in his review session. At that time, I didn't quite get it.

But now I get it!!

People learn from their mistakes. It's true. I've at least fixed this problem, and I hope this mistake helps my future courses such as CSC236.

There are several other things that I made mistakes on Assignment-2 need to be mentioned and noted in this blog to make sure I will not make the same mistakes during the final exam.

And again, check out latex.codecogs.com. This is a great and easy way to implement math equations on the web!!

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