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A proof is presented for the absence of gap for spin $1/2$ ladders with anodd number of legs, in the infinite leg length limit. This result is relevantto the current discussion of coupled one--dimensional spin systems, a physicalrealization of which are vanadyl pyrophosphate, (VO)$_2$P$_2$O$_7$, andstoichiometric Sr$_{n-1}$ Cu$_{n+1}$ O$_{2n}$ (with $n=3,5,7,9,\dots$).Comment: REVTeX, 8 page

Absence of gap for infinite half-integer spin ladders with an odd number of legs