Math Help - uncountability

1. uncountability

We want to prove that $[a,b]$ and $(a,b)$ are uncountable.

The book says that there are bijections from $(a,b)$ onto $(-1,1)$ onto unit semicircle. From this point how do we deduce that $(a,b)$ is uncountable?

$[a,b]$ is then uncountable if we prove that $(a,b)$ is uncountable.

2. Originally Posted by shilz222
We want to prove that $[a,b]$ and $(a,b)$ are uncountable.

The book says that there are bijections from $(a,b)$ onto $(-1,1)$ onto unit semicircle. From this point how do we deduce that $(a,b)$ is uncountable?

$[a,b]$ is then uncountable if we prove that $(a,b)$ is uncountable.
The diagnol argument shows that $(0,1)$ is uncountable. That that means $(-1,1)$ is uncountable because it contains it as a subset.