# Truth value of statement

1. Mar 22, 2008

### Lococard

1. The problem statement, all variables and given/known data
Determine the truth value of the statement.

There exists x for every (xsquared smaller than y+1)

x and y a set of non-negative real numbers

Sorry i dont know how to do the maths symbols on the computer.

2. Relevant equations

All the numbers i have used make the statement true. The teacher said to try and proove the statement false, rather than prooving it correct.

Another teacher said it is to do with fractions.

3. The attempt at a solution

As above

2. Mar 22, 2008

### Gib Z

Is that the question as it was given? Is the question;

Show that there exists a value of x such that for every value of y, $x^2 < y+1$ ?

If that is the question, the statement is actually true.

3. Mar 22, 2008

### Lococard

Ah ok.

How would i prove this?

I looked at a few of the proven workings but nothing resembles a similar question?

4. Mar 22, 2008

### Gib Z

To prove it: Since y must be a non-negative real number, the smallest the RHS can be is 1. So every single time it suffices to choose a value of x^2 less than 1, which is a value of x less than 1.

5. Mar 22, 2008

### CompuChip

In fact any number $x < \sqrt{y + 1}$ would do. If you'd want to be dull you could just take x = 0 for all y.