- #1

daniel_i_l

Gold Member

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**an "infinite" amount of permutations,**

Look at how the sum of the alternating harmonic series can be changed by rearranging the terms:

http://mathworld.wolfram.com/RiemannSeriesTheorem.html

But doesn't this involve a non-finite amount of permutations? If this counts as a rearrangement then why can't we change 0,1,0,1... into 0,0,0... by the following argument:

If we know that for a sequence a_n, for every N>0 for every n<N a_n = 0 then obviously

a_n = 0,0,0... right?

But suppose we take the sequence b_n = 1,0,1,0... Then with N permutations (it doesn't really matter how many) we can rearrange it so that the first N elements are 0. So with an "infinite" amount of permutations we can make the first N elements 0 for all N!

I'm pretty sure that the problem here is in the expression "infinite amount of permutations" but I can't see any way to describe the rearrangement on wolframs site. Can someone help me clear this up?

Thanks.