" ((a, b), (c, d)) " R Ô! a - b = c - d.
(a,b),(c,d)"N×N
R ‚" (N×N)×(N×N) X = N×N
Z = N × N|R
[(a, b)] + [(c, d)] = [(a + c, b + d)],
[(a, b)] · [(c, d)] = [(ac + bd, ad + bc)].
" ((a, b), (c, d)) " R Ô! ad = bc.
(a,b),(c,d)"Z×N
R ‚" (Z×N)×(Z×N) X = Z×N
Q = Z × N|R
[(a, b)] + [(c, d)] = [(ad + bc, bd)],
[(a, b)] · [(c, d)] = [(ac, bd)]
(an)n"N ‚" Q
" " " | am - an |< µ.
µ>0 n0"N m,n"N,m,n>n0
C(Q)
" ((an), (bn)) " R Ô! " " " | an - bn |< µ.
µ>0
(an),(bn)"C(Q) n0"N n"N,n>n0
R ‚" C(Q)×C(Q)
R = C(Q)|R
[(an)] + [(bn)] = [(an + bn)],
[(an)] · [(bn)] = [(an · bn)].