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Ricky Y.

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Bijection

f is bijective if f is both injective (1 to 1) and surjective (onto).

Set Equivalence

Function f:A->E which is One-to-One and onto

Equivalence Relation

Reflexive, Symmetric, and Transitive

Reflextive

x~x, all x in A

Symmetric

x~y, y~x

Transitive

x~y, y~z-> x~z

Definition: Equivalence relation, equivalence class, quotient space

***

Peano Properties

Peano Isomorphism

Addition

A1 in N

A2 in N

Ordering in N

Trichotomy

cancellation in N

Subtraction in N

Multiplication

Def of Z

Addition in Z

A3 in Z

A4 in Z

N* in Z

Ordering in Z

Multiplication (Dot Product)

Def of Q

Addition in Q

0 in Q

1 in Q

-x in Q

Multiplication in Q

x^-1 in Q

x/y in Q

Q+

Ordering in Q

R

Lower Section

Upper Bound

Least Upper Bound

Lower Bound

Greatest Lower Bound

Subsequence of {xn}

Limit of a sequence

Continuity of f

Ordering in R

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