... a∈H , then it is trivial If a∈G\H , then consider that aH and Ha Now ,since [G:H]=2 ,so we have that G=HUHa=HUaH...
...f: {0, 1}→N, every f can have at most 2 different values. i.e. every f is such that f(0)=p, f(1)=q for all p, q in N. Now we denote the function f where f(0)=p and f(1)=q by [p, q]. then we can arrange them in this form: [1, 1], [1, 2], [1, 3], [1, 4], ... [2, 1...
... that (1 2)(1 3 )=(1 3 2). Now HK={hk: h in H and k in K}={ (1), (1 2) , (1 3), (1 3...補充： Correct my misprint : Every associative binary structure(it is a...
...a multiple of 3. We claim that from now on, the number of stones in...by merging the piles with 5 and 51 stones, then the number of stonesin every subsequent pile must be a multiple of 7. If...
... result holds for every x is real because rational.... Suppose x and y are real, r and s...rational with r≦x and s≦y. Then (r+s) ≦ (x+y) , so(b^r...that (b^x)(b^y) ≦ b^(x+y) Now , suppose that t is rational...
...that Rn=x when n even and Rn=1 when n odd. Now we prove it by induction. x...-1)+xRn Then you can finish the induction... is a group, every number is invertible...
...mod3) iff b^i=b^j . If f(a^i)=f(a^j), then b^i=b^j, so i≡j (mod3), and , now we have a^i = a^j. Hence, f is... isomorphic. Concluded that every group of order 3 are isomorphic.
...whenever |x-0| less than delta.}. Now we shall prove that the limit...the contrapositive statement [~q then ~p] of {...}: for some epsilon (positive) given, for every positive delta we will find...], at this x, f(x)=1 and hence |f(x)-L|=|f...
