I know that $\mathbb{R}$ represents the set of all real numbers. But what does $\mathbb{R}^2$, $\mathbb{R}^3$, ..., $\mathbb{R}^n$ mean?
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2$X^n$ is the set of $n$-tuples of elements of $X$. – Sassatelli Giulio Nov 04 '22 at 11:03
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2See this: https://en.wikipedia.org/wiki/Cartesian_product in "n-ary Cartesian power" paragraph. – asv Nov 04 '22 at 11:04
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1Maybe not a duplicate, but possibly of interest: What is the definition of $\mathbb{R}^{n}$? – Andrew D. Hwang Nov 04 '22 at 14:06
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As you pointed out $\mathbb{R}$ is the set of all real numbers. $\mathbb{R}^n$ is the cartesian product of $n$ many $\mathbb{R}$'s. It's the set of tuples $(x_1, x_2, \ldots, x_n)$ where each $x_i$ is a real number.
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