# Math Help - Least Element

1. ## Least Element

Let $n_0\in\mathbb{Z}$, S is nonempty subset of $T=\left(n\in\mathbb{Z}|n\geq n_0\right)$ and l* is a the least element of the set $T^*=\left(n-n_0+1|n\in S\right)$. Then $n_0+l+1$ is a least element of S.

I am not sure how to go about this one.

2. Originally Posted by dwsmith
Let $n_0\in\mathbb{Z}$, S is nonempty subset of $T=\left(n\in\mathbb{Z}|n\geq n_0\right)$ and l* is a the least element of the set $T^*=\left(n-n_0+1|n\in S\right)$. Then $n_0+l+1$ is a least element of S.

I am not sure how to go about this one.
Just show that $n_0+l+1$ is indeed a lower bound for $T$ and if it weren't the least element that there would be something smaller, and show that this something smaller with a slight modification would be an element of $T^*$ smaller than $n_0+l+1$.