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I was able to enumerate all the subcomplexes of S^{infinity}, where S^{infinity} has two 0-cells, two 1-cells, two 2-cells, etc. But how do I show that S^{infinity} is contractible?

Can anyone point me in the right direction? X is contractible if and only if the identity map of X is homotopic to a constant map.

I guess I don't see what kind of homotopy (a shrinking map) I need to set up between X and a point.

Thank you!