I'm reading the book Basic Set Theory by: Azriel Levy as I thought it might help me better understand Group Theory and Matrix Math. I have read the first chapter a number of times but I keep getting hung up on some of the syntax of the basic language or language of first-order predicate calculus with equality.(adsbygoogle = window.adsbygoogle || []).push({});

In the first two pages I get stuck on this:

i) [tex] \exists x\left ( x \in y \land \phi \right ) [/tex]

where this is read "there is an x in y such that phi!"

Such that phi what? I mean there are a lot of things I understand about what is being laid out in the language of first order logic such as:

ii) [tex] \phi \land \psi [/tex] is [tex] \lnot ( \lnot \phi \lor \psi ) [/tex]

but again I have trouble with i).

I really thought I would get somewhere with this book and still probably will over a lengthy period of time. Is there something else I should be addressing first? What does i) mean? Where are all these brackets coming from and where were they supposed to have been defined?

iii) [tex] R[A]=\left \{ y| \left ( \exists x \in A \right ) \left ( <x, y> \in R \right ) \right \} [/tex]

There were lengthier examples! I think the brackets and the sudden realization of functions of the basic language are my two biggest hangups in being able to understand the full depth of the axioms being presented; many of which I have some vague understanding of from their general use in other subjects. Advice [tex] \land \lor [/tex] explanation of my above two dilemmas? :/

thx,

BekaD:

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# Set Theory: Basic Language

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