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Apr 18, 2010 at 21:57 comment added Glen M Wilson I think you mean: "Multiply each $g_i$ by a smooth function $h$ equalling 1 on a neighborhood of 0 and vanishing elsewhere. Then $hg_i\in I_p$, so that $f$ munius a linear combination of terms $(hg_1)\cdots (hg_n)$ vanishes in a neighborhood of $0$.
Apr 16, 2010 at 23:37 vote accept Glen M Wilson
Apr 16, 2010 at 21:14 history answered Robin Chapman CC BY-SA 2.5