> See <https://math.stackexchange.com/questions/415787/motivation-of-stable-homotopy-theory>

**Fiber and Cofiber sequences Agree** There is a theorem of Blakers and Massey, sometimes called homotopy excision which says: even though taking homotopy groups does _not_ take [cofiber sequences](cofiber%20sequences) to long exact sequences, it does do so in a certain range depending on the connectivity of the cofiber sequence.   

In particular, if we keep suspending the cofiber sequences (in which case we're asking about [stable homotopy](stable%20homotopy.md) groups) then this _is_ the case. This turns out to be enormously useful (think about every time you make an argument in homology using the long exact sequence of a pair... you can now make that argument with stable homotopy groups, or any other nice [spectrum](spectrum), etc.)