Let $t \in \mathbb{R}$ and let $\epsilon >0.$ Let $g_1(x) = 1$ on $(\infty, t)$ and $0$ on $[t+ \epsilon, \infty).$ Let $g_2(x) = 1$ on $(-\infty, t - \epsilon]$ and $0$ on $[t, \infty).$
Something I am reading says that $g_1$ and $g_2$ form upper and lower "envelopes" for $\mathbf{1}_{(-\infty, t]}.$
What does this mean? I tried graphing it but I am not seeing what "envelopes" mean.
Thanks.