# Properties of Real Numbers

## 20 terms

a=a

If a=b, then b=a

### transitive property of equality

If a=b and b=c, then a=c

If a=b, then a+c=b+c and c+a=c+b

### multiplication property of equality

If a=b, then ac=bc and ca=cb

### closure for addition or multiplication

a+b are unique real numbers

### commutative for addition or multiplication

a+b=b+a and ab=ba

### associative for addition or multiplication

(a+b)+c = a+(b+c) and (ab)c=a(bc)

### identity for addition or multiplication

There are unique real numbers 0 and 1 (1 doesn't = 0) such that: a+0=a and 0+a=a, and also a(1)=a and (1)a=a

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### distribution (of multiplication with respect to addition)

a(b+c) = ab+ac and (b+c)a = ba+ca

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a-b=a+(-b)

a/b=(a)1/b

### multiplicative property of 0

a(0)=0 and (0)a=0

### multiplicative property of -1

a(-1)=-a and (-1)a=-a

### property of the opposites of a product

-ab=(-a)b and -ab=a(-b)

(-a)(-b)=ab

### property of the opposite of a sum

-(a+b) = (-a)+(-b)