已知集合M={x丨x=(5k+3)/5,k∈Z},N=｛x丨x=(5k-2)/5,k∈Z｝,求证M=N

已知集合M={x丨x=(5k+3)/5,k∈Z},N=｛x丨x=(5k-2)/5,k∈Z｝,求证M=N

M:
x=(5k+3)/5,k∈Z
=k+3/5,k∈Z
N:
x=(5k-2)/5,k∈Z
=k-2/5,k∈Z
令k=t+1,t∈Z
∴x=t+1-2/5=t+3/5,t∈Z
∴N={x=t+3/5,t∈Z}
M=N