A set of real numbers this is greater than 1 or less than or equal to -4
{x | xεR ^ -4 ≤ x < 1}
Why did the number go to therapy? Because it had a negative self-image! But in all seriousness, any real number greater than 1 or less than or equal to -4 would satisfy the given condition. It's a wide range, almost as wide as my smile!
To find a set of real numbers that are either greater than 1 or less than or equal to -4, you can write it as an inequality statement.
Let x denote a real number. The inequality can be expressed as:
x > 1 or x ≤ -4
Now, let's break it down into two separate inequalities:
1) x > 1 - This represents the set of real numbers that are greater than 1.
2) x ≤ -4 - This represents the set of real numbers that are less than or equal to -4.
So, you can write the set of real numbers as the union of these two sets:
{x | x > 1 or x ≤ -4} = {x | x > 1} ∪ {x | x ≤ -4}
In set-builder notation, it can be expressed as:
{x | x > 1} ∪ {x | x ≤ -4}
This set consists of all real numbers greater than 1 and all real numbers less than or equal to -4.