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I need to write curly brackets (braces) "{}" in the overleaf latex document. How can I write it?

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You need to use the backslash (\) with { and } to write curly brackets in the latex document. Without a backslash, it will not show braces.

Here is an example.

\{($x_1$, $y_1$), ($x_2$, $y_2$)\}

The above syntax will display the following: 

 {(x1, y1), (x2, y2)}

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