Let n be a positive integer. Let H = {0, n, 2n, 3n, ...}. Find all left cosets of H in Z. How many are there?

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Let n be a positive integer. Let H = {0, n, 2n, 3n, ...}. Find all left cosets of H in Z. How many are there?

abstract algebra

2007-12-02 05:48:39 · 2 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics

2 answers

That's a a trick question. There are infinitely many; every integer gives a unique left coset. Why? Because each of those cosets has a different smallest element!

If H contained ALL multiples of of n, that would be a very different matter; then there would only be n cosets in total.

2007-12-02 07:16:34 · answer #1 · answered by Curt Monash 7 · 0⤊ 0⤋

ideal, i will not be able to write with my left hand in any respect! yet I do a great type of issues with my left hand, curiously i'm left hand eye co-ordinated. Or ideal, whichever is the choice of what ideal handers must be! I open doorways, carry luggage and do maximum stuff with my left hand.

2016-12-10 10:08:48 · answer #2 · answered by ? 4 · 0⤊ 0⤋