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I'm not an expert in this field, but are the following true and could be added to the article:

1) The homotopy groups of the sphere spectrum are the stable homotopy groups of the spheres.

2) In the homotopy category, [X,Y] is a module over the (stable) homotopy ring of the sphere spectrum.

I think there should be some hints in this article, why this spectrum is so important and interesting.

Best regards, Ringspectrum (talk) 10:00, 17 January 2009 (UTC)[reply]