cohomotopy result

if f and g are two smooth functions from a smooth manifold M^n->S^p,
and we have the condition
that |f-g|<2 then f and g are smoothly homotopic. I think I
understand
that in this case f and g
are both members of a cohomotopy group, but the significance of <2
evades me. Clearly, if
|f-g|>2, then either one of both of the maps don't map onto the n-
sphere, if |f-g|=2, then f,g
map to antipodal points, but don't see right away why that scotches
their being homotopic.

Thanks in advance for any suggestions on the significance of the
inequality condition.

.

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