Proprietatile adunarii:
1.asociativitatea: (x+y)+z=x+(y+z) oricare ar fi x,y,z ∈ R
(1+2)+3=1+(2+3)
3+3=1+5
6=6
2.comutativitatea: x+y=y+x oricare ar fi x,y ∈ R
1+2=2+1
3=3
3.0 element neutru: x+0=0+x=x oricare ar fi x ∈ R
1+0=0+1=1
1=1=1
4. element opus: oricare ar fi x ∈ R si -x ∈ R astfel incat
x+(-x)=(-x)+x=0
1+(-1)=(-1)+1=0
0=0=0
Proprietatile inmultirii:
1.asociativitatea: (x·y)·z=x(y·z) oricare ar fi x,y,z ∈ R
(2·3)·4=2(3·4)
6·4=2·12
24=24
2.comutativitate: xy=yx oricare ar fi x,y ∈ R
2·3=3·2
6=6
3.1 element neutru: x·1=1·x=x oricare ar fi x ∈ R
2·1=1·2=2
2=2=2
4. element invers: oricare ar fi x ∈ R*, 1 1 1
---- ∈ R* astfel incat x · ---- = ---- · x = 1
x x x
Distributivitatea inmultirii fata de adunare si scadere:
x(y+z)=xy+xz oricare ar fi x,y,z ∈ R
2(3+4)=2·3+2·4
2·7=6+8
14=14
