Prove that the statement is false:
"There exists a real number y such that for every real number x, y < x."
I tried to prove this statement to be false, but no matter what counterexample I try to come up with it doesn't work.
do you understand the statement ... maybe its not false
let y = x-1
clearly, y < x no matter what x is.
To prove that the statement is false, you need to show a counterexample that contradicts the statement. Let's analyze the statement: "There exists a real number y such that for every real number x, y < x."
To find a counterexample, we first negate the statement: "For every real number y, there exists a real number x such that y is not less than x." This is equivalent to saying that no matter which real number y you choose, there will always be a real number x such that y is not less than x.
Now, let's suppose there is a real number y such that for every real number x, y < x. This would mean that no matter what x we choose, y will always be less than x. However, this is not possible because there is no real number y that is less than every real number x.
In the real number line, you can always find a real number x that is greater than any given real number y. For example, if y = 1, you can choose x = 2, and y is not less than x.
Since we have found a counterexample that contradicts the statement, we have proven that the original statement is false.