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# 19 Revisions

 Apr 12 revised How many one to one functions? Fixed LaTex Apr 11 revised How to simplify the expression $(\log_9 2 + \log_9 4)\log_2 (3)$ Helped with the LaTex. Jul 4 revised Let $f=g$ on $[a,b]/E$ where $f\in \mathcal{R}[a,b]$ and continuous on $[a,b]$. Then $g\in\mathcal{R}[a,b]$ and $\displaystyle\int_a^b f=\int_a^bg$. added 148 characters in body Jul 4 revised Let $f=g$ on $[a,b]/E$ where $f\in \mathcal{R}[a,b]$ and continuous on $[a,b]$. Then $g\in\mathcal{R}[a,b]$ and $\displaystyle\int_a^b f=\int_a^bg$. added 98 characters in body Feb 17 revised Did I do this proof right? Here is one proof. Jan 6 revised Tonelli and Fubini and almost everywhere added 65 characters in body Oct 6 revised Showing $\mathbb{Z}[\frac{1+\sqrt{D}}{2}]$ is a subring added 45 characters in body Oct 2 revised Center of finite group with 3 conjugacy classes has order 1 added 224 characters in body Jul 28 revised Diagonal matrices and integrals deleted 12 characters in body Jul 28 revised Diagonal matrices and integrals deleted 12 characters in body Jul 27 revised Fundamental Theorem of Calculus and limit deleted 4 characters in body Dec 6 revised Divergence of the series $2^{-1/n}$ added 117 characters in body Dec 6 revised Divergence of the series $2^{-1/n}$ added 212 characters in body Dec 6 revised Divergence of the series $2^{-1/n}$ added 212 characters in body Nov 4 revised Squeeze Theorem conclusion deleted 135 characters in body Nov 21 revised Proof on limits using Cauchy sequences deleted 67 characters in body Sep 3 revised Points being collinear edited body Apr 8 revised The set of all permutations of a set is a group example deleted 1 characters in body Feb 13 revised Show that an operation being commutative is a structural property added 126 characters in body; edited title