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 Nov 1 revised Two quotients of projective modules are equal, prove the crossed direct sums of the projective modules and kernels are isomorphic. (Schanuel's Lemma) edited title Nov 1 comment Two quotients of projective modules are equal, prove the crossed direct sums of the projective modules and kernels are isomorphic. (Schanuel's Lemma) Great, thanks!! Nov 1 asked Two quotients of projective modules are equal, prove the crossed direct sums of the projective modules and kernels are isomorphic. (Schanuel's Lemma) Oct 29 revised Every open set in $\mathbb{R}$ is the countable union of rational open intervals added 4 characters in body Oct 29 revised Every open set in $\mathbb{R}$ is the countable union of rational open intervals added 879 characters in body Oct 29 answered Every open set in $\mathbb{R}$ is the countable union of rational open intervals Oct 28 revised Are there any real life applications of the greatest common divisor of two or more integers? deleted 5 characters in body Oct 20 awarded Notable Question Oct 19 awarded Notable Question Oct 15 comment If $3|n^3$, does $3|n$? While this is a good argument, the fundamental theorem of arithmetic is usually proved by using this result (a variation of it at least). Oct 15 answered If $3|n^3$, does $3|n$? Oct 13 comment How many six-digit numbers are there such that their sum of digits is $\le 47$? Instead of seeing how many "ones" we put inside each position we can see how many "ones" we do not put in each position (assuming we start with $9$ "ones" in each position). This rids us of the "upper bound" problems when we look at it in the straightforward approach. A final "trick" we can use is the known identity $\sum_{i=0}^k\binom{n+i}{n}=\binom{n+k+1}{n+1}$. Oct 13 answered How many six-digit numbers are there such that their sum of digits is $\le 47$? Oct 10 awarded Famous Question Oct 8 comment If $f$ is odd how does this imply that $f$ is symmetric about the origin in polar coordinates? Symmetric about the origin is not the same as symmetric about the y-axis, I think this may be the cause for your confusion. Oct 8 comment Topologies on a finite set with the same number of open sets If you apply a permutation to the topology you are going to get a topology homeomorphic to the original one. Oct 8 comment Topologies on a finite set with the same number of open sets What is $|\tau|$? Oct 8 answered The product of $2×653×733×977$ has each digit exactly once except for one, which one is it? Oct 8 comment In how many ways can we select $x$ distinct candies from a collection of $n$ candies of distinct types? I assume the candies from each jar are identical between each other and candies from different jars are distinct, is this assumption correct? Oct 8 answered $\frac{(mn)!}{m!(n!)^m}\in\mathbb N^*$?