[Solved]: Period in postulate; what does it mean?

Problem Detail: 

While I am learning a lot from others here at the Computer Science site, I must admit that I don't get as much out of some questions and answers since I typically don't understand the theorems to the level necessary. I am currently reading How To Prove It - A Structured Approach which is starting to make the theorems easier to read, but still does not get me to the point of being able to understand the theorems to the point that they add great insight to the question or answer.

For this question Is it possible to always construct a hamiltonian path on a tournament graph by sorting?

there is a use of a peroid in the premise.

$\qquad \displaystyle a \leq b \iff (a,b) \in E \lor \left(\exists\, c \in V. a \leq c \land c \leq b\right)$

What does the period mean? I would be expecting either a comma to mean conjuction or or to mean disjunction, but not a period. I don't see how this could be converted to logical statements.

Note: Jukka Suomela has already provided the answer in this CS meta question.

Asked By : Guy Coder

Answered By : Dave Clarke

After an $\exists$ the period can be read as "such that". For example, $\exists x\in \mathbb{N}. x>4$ can be read as "there exists a natural $x$ such that $x$ is greater than 4."

After a $\forall$ it can be read as "it is the case that". For example, $\forall x\in\mathbf{N}. x + 1> x$ can be read as "for all natural numbers $x$, it is the case that $x+1$ is greater than $x$.

Generally one can omit "it is the case that" and the sentence still works.

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Question Source : http://cs.stackexchange.com/questions/2962