User:Sunil pasupulati/Sandbox

real numbers
set of Real numbers is super set of natural numbers,whole numbers,integers,rational numbers,irrational numbers. set of real numbers is field under operations +,..

set of real numbers satisfy all field properties

 field properties 

for every a belong to a,b,c belong to R

1.a+b=b+a(commutative law with respect addition )

2.a.b=b.a(commutative law w.r.t multiplication )

3.a+(b+c)=(a+b)+c(associative law w.r.t addition)

4.a.(b.c)=(a.b).c(associative law w.r.t multiplication )

5.there exists "0" such that a+0=a

6.there exists "1" such that 1.a=a

7.there "-a" for every "a" such that a+(-a)=0

8.there "1/a" for every "non zero a" such that a.1/a=1 9.a(b+c)=ab+ac

 order properties 

1.law of trichotomy

2.a<b,b<c then a<c

3.if a<b ,then a+c<b+c

4.if a<b then ac 0