weekly homework
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\begin{document}
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\title{Weekly Homework 1}%replace X with the appropriate number
\author{Joey Stockdill\\ %replace with your name
Introduction to Abstract Math} %if necessary, replace with your course title
\maketitle
\begin{theorem}{2.15} %You can use theorem, exercise, problem, or question here. Modify x.yz to be whatever number you are proving
An odd integer times an odd integer results in an odd integer.
\end{theorem}
\begin{proof} %You can also use solution in place of proof.
Assume m and n are both odd integers.\\
Let m = 2k+1, and n = 2j+1\\
So mn = 4kj+2k+2j+1\\
Which factors into 2(2kj+k+j)+1.\\
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By definition 2.9 (2kj+k+j) is an integer.\\
so by definition 2.10 mn is an odd integer.\\\\
\end{proof}
\begin{theorem}{2.12} %You can use theorem, exercise, problem, or question here. Modify x.yz to be whatever number you are proving
The product of an odd integer and an even integer is odd.\\\\
\end{theorem}
\begin{proof} %You can also use solution in place of proof.
The product of 2 times 3 is 6, which is an even number.
\end{proof}
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