Hello I am just having a quick question
in the textbook intro to real analysis, during one of the limit examples the author notes,
if $$|x-c| \lt 1$$ then $$|x| \lt |c| +1$$
What rules are used to say this? how can I be rigour sure this is true.
For context, the c is just a constant. Thanks everyone
$|x| = |x-c+c|$
By triangle inequality, $|x| \le |x-c|+|c| < |c| + 1$