Originally Posted by

**Krahl** i guess not since saying that the agm are equal is saying that the corresponding sequences have the same limit, but there are multiple different sequences which have the same limits.

for example if you have the sequence from (a,b) then you can find 2 numbers c and d such that they satisfy a_n=g_n for some n. so (c,d) will give rise to a sequence not equal to the first but has the same agm. but there may be many such iterations a_n and g_n.in this case (c,d) would give rise to a subsequence of the first.