la partie entier

montrez les proposition s suivantes

°[x+y]>=[x]+[y]

°[x-y]<=[x]-[y]

°[[x]/n]=[x/n]

(x:y)£R² et n £N*

posant x=n+r et y=p+q (p.n £N² 0<=r<1 0<=q<1)
[x]+[y]=n+p
[x+y]=[n+p+q+r]=n+p+[q+r] (0<=q+r<2]
[q+r]>=0
[x+y]>=[x]+[y]

[x-y]=[n-p+r-q]=n-p+[r-p] ( -1<=r-p<1)
[r-p]<=0
<=>[x-y]<=n-p=[x]-[y]

pose a=[x] et b=(x-a )£ [0.1[