I have $$a_i^t-a_i^*=\sum_{b\in B}b+\sum_{c\in C}c,\\B\ne C,\\B, C \subset R$$ Can I say that $$|a_i^t-a_i^*|\le\sum_{b\in B}|b|+\sum_{c\in C}|c|?$$
2026-02-23 02:46:59.1771814819
Triangle inequality in sum of summations
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The triangle inequality implies $\left|\sum_{i=1}^n x_i\right| \le \sum_{i=1}^n |x_i|$ for any real numbers $x_1, \ldots, x_n$. Your inequality follows from a direct application of this fact.