Find the flaw with the following \"proof that every postage of three cents or mo

Question

Find the flaw with the following "proof that every postage of three cents or more can be formed using just three-cent and four-cent stamps. Basis Step: We can form postage of three cents with a single three-cent stamp and we can form postage of four cents using a single four-cent stamp. Inductive Step: Assume that we can form postage of j cents for all nonnegative integers j with j lessthanorequalto k using just three-cent and four-cent stamps. We can then form postage of k + 1 cents by replacing one three-cent stamp with a four-cent stamp or by replacing two fourcent stamps by three three-cent stamps.

Explanation / Answer

There is a flaw in the inductive step. BEcause there is no information given about k ie the smallest value k can take because for k=5 we cannot have 3 and 4 cents form k=5 so assuming for all j<=k we can form all postages is wrong without giving any information about bounds for k

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