How can I prove that $|x_ny_n-xy| \leq |x||y_n-y|+|y_n||x_n-x| $ ?
2026-04-02 07:56:56.1775116616
Modular inequality of sequential terms: $|x_ny_n-xy| \le |x||y_n-y|+|y_n||x_n-x|$
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$$x_ny_n-xy=x(y_n-y)+y_n(x_n-x)$$ and then use triangle inequality (norm properties).