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This is an inline equation: \(x^2=-1\).
This is a centered equation: \[a^2+b^2=c^2.\]
This is a numbered equation: \[\begin{equation} \lim_{n\to\infty}\frac{1}{n}=0. \label{eq:sample} \end{equation}\]
This is an aligned equation: \[\begin{align} \int_{0}^{1}2x\,dx &=x^2\Big|_{x=0}^1\label{eq:sample2}\\ &=1 \end{align}\]
This is how to cite the above equation: \(\eqref{eq:sample}\) & \(\eqref{eq:sample2}\).
Theorem 1. This is a theorem environment.
Corollary 2. This is a theorem-like environments.
This is how to cite the above theorem: Theorem 1 & Corollary 2.
Proof. Here goes the proof. ◻
This is how to cite references: (Mac Lane, n.d.).
Mac Lane, Saunders. n.d. Categories for the working mathematician. Vol. 5. Springer Science & Business Media.