Answer by Michael Hardy for Prove that if every PROPER sub sequence of a...
If every proper subsequence of $a_1,a_2,a_3,a_4,\ldots$ is convergent then $a_2,a_3,a_4,\ldots$ is convergent. But if $a_2,a_3,a_4,\ldots$ is convergent, then so is $a_1,a_2,a_3,a_4,\ldots$, and it has...
View ArticleAnswer by ploosu2 for Prove that if every PROPER sub sequence of a sequence...
Just leave the first term out, that's a proper subsequence :D.
View ArticleAnswer by Julián Aguirre for Prove that if every PROPER sub sequence of a...
Suppose there are two subsequences that converge to different limits. Create a new subsequence by mixing the terms of the two subsequences. Is this new subsequence convergent?
View ArticleProve that if every PROPER sub sequence of a sequence is convergent , then...
Prove that if every PROPER sub sequence of a sequence is convergent , then the sequence is convergent. ( By proper, i mean all the sub sequences excluding the main sequence )$Attempt$ : Since all...
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