First Order Logic Resources

Tutorials

 * 1) Rules and terminology by Wolfram Mathworld [FOL]
 * 2) Some [good note]s on how to start with FOL (very programming oriented)
 * 3) Peter Suber's [translating logic into English AND his [glossary] of set theory is immensely helpful for the uninitiated.


 * 1) [PD Magnus] forall x: an introduction to formal logic.


 * 1) Thorough intro, but very "textbookish" below

  First-Order_Logic

Symbols in Logic
This chart can be found on the [wikipedia page]

Logical Operator With Venn Explanations
[Wikipedia Page] is really best resource.

Set Theory
* $$\{a \in \mathbf A }$$ is used to denote that a is an element of a set  A.


 * $$\{x \in \mathbf R: x = x^2 \} \,\!$$ is the set $$\{0, 1\}$$,
 * $$\{x \in \mathbf R: x > 0\}$$ is the set of all positive real numbers.

Cardinal Number

In formal set theory, a cardinal number (also called "the cardinality") is a type of number defined in such a way that any method of counting sets using it gives the same result. (This is not true for the ordinal numbers.) In fact, the cardinal numbers are obtained by collecting all ordinal numbers which are obtainable by counting a given set.

Function

A function is a relation that uniquely associates members of one set with members of another set. More formally, a function from to  is an object  such that every  is uniquely associated with an object. A function is therefore a many-to-one (or sometimes one-to-one) relation. The set of values at which a function is defined is called its domain, while the set  of values that the function can produce is called its range. The term "map" is synonymous with function

Basic Calc
Integral - An integral is a mathematical object that can be interpreted as an area or a generalization of area. Integrals, together with derivatives, are the fundamental objects of calculus. Other words for integral include antiderivative and primitive

Derivative - The derivative of a function represents an infinitesimal change in the function with respect to one of its variables.

The "simple" derivative of a function with respect to a variable  is denoted either  or

d f -- dx