Question

Consider the interval [0, infinite symbol) . For each numerical value. Is it interval or not.

Answer 1

Since the given interval is

`\lbrack0,\infty)`

Then any number starting from zero to infinty belongs to it

The interval has zero and all positive real numbers

1) The given number is

`-4.2*10^5`

Since the number is negative, then it does not belong to the given interval

`-4.2*10^5\\otin\lbrack0,\infty)`

2) The given number is

`10^(-3)`

Reciprocal it to change the sign of the power from negative to positive

`10^(-3)=(1)/(10^3)=(1)/(1000)`

Since the number is positive, then it belongs to the given interval

`10^(-3)\in\lbrack0,\infty)`

3) The given number is

`\lvert-8.5\rvert`

Since the absolute neglect the sign of the number, then

`\lvert-8.5\rvert=8.5`

Then the number is positive, so it belongs to the given interval

`\lvert-8.5\rvert\in\lbrack0,\infty)`