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# Calc 1

### Vocab List 1-11

Commutative For every x,y belonging to F, there is a x+y=y+x and a x*y=y*x
Associative For every x,y,z belonging to F there is: (x+y)+z=x+(y+z) and (x*y)*z=x*(y*z)
Closure For every x,y belonging to F there is x+y belonging to F and x*y belonging to F.
Well-Ordering Principle -Every non-empty sub set of Natural Numbers has a least element. -If M <= Natural Numbers, then there exists R belonging to M so that R <=a for ever a belonging to M.
Induction Principle (Natural Numbers) Suppose P(n) is a statement about: n belonging to Natural Numbers, If we can show 1.P(1) is true. 2.Whenever P(n) is true then P(n+1) is true. Then P(n) is true for all n.
Ordered Field A field F that is an ordered set with the following additional properties: 1. If x>0 and y>0 then x+y>0 2. If x>0 and y>0 then x*y>0 3. x<y if and only if y-x>0
Order An order on a set S is a relation that satisfies the following: 1. If x,y belongs to S, then exactly one of x<y, x=y, or y<x is true. 2. For all x,y,z belonging to S, if x<y and y<z then x<z.
Field A nonempty set F of objects that has two operations, addition and multiplication, that satisfy the following properties: -Closure -Associative -Identity -Inverses -Distributive -Commutative
Distributive For every x,y,z belonging to F there is x*(y+z)= x*y + x*z
Inverses For every x belonging to F there is -x belonging to F so that x+(-x)=0 For each x belonging to F there is a 1/x belonging to F so that x* (1/x) = 1, x!=0.
Identity For x belonging to F there exists 0 belonging to F so that x+0=x and there exists 1 belonging to F so that x*1=x.
Created by: rissa230