Is this [-8,infinity) the same as this x < -8 OR x > 1 ? Thank you.
[-8,infinity)
is the same as 0≤8<∞
[ and ] include the respectivelimites,
( and ) exclude
erratum:
[-8,infinity)
You can also see
http://www.jiskha.com/display.cgi?id=1248473985
is the same as 0 ≤ -8 < ∞
[-8,infinity)
is the same as
-8 ≤ x < ∞
x < -8 OR x > 1
is
(-∞,-8) &cup (1,∞)
So they are not the same.
To determine if the interval [-8, infinity) is the same as the inequality x < -8 OR x > 1, we need to understand the meaning of both expressions.
The interval [-8, infinity) represents all the numbers greater than or equal to -8. The square bracket indicates that -8 is included in the interval, and the parenthesis indicates that infinity is not included.
On the other hand, the inequality x < -8 OR x > 1 represents two separate conditions. The first condition, x < -8, means that x can be any number less than -8, but does not include -8 itself. The second condition, x > 1, means that x can be any number greater than 1.
Comparing the two expressions, we can see that the interval [-8, infinity) includes -8 but also includes all numbers greater than -8. In contrast, the inequality x < -8 OR x > 1 does not include -8, and it includes two separate ranges, numbers less than -8 and numbers greater than 1.
Therefore, [-8, infinity) is not the same as x < -8 OR x > 1.