finding a number that satisfies given conditions

I need to find a floating point number x from the interval 1 < x < 2 such that: x ∗ (1/x) isn't equal to 1. I'ma beginner at Matlab and don't know how this can be done. I was given a clue that using integrals could help in solving this. Could anyone help me?

[Cedric]

What is the symbol/operator between the x and 1/x ?

[Walter Roberson]

Multiplication, I would say. Looks like an exercise in exploring the limits of binary floating point representation.

[Beaya]

I wrote a program to do this in C, but I must have done something wrong because the result was: 4.94066e - 324, which is smaller than 1.

Answer 1

[Mike Hosea]

Integrals? Not sure about that. A random search will finish faster. There are LOTS. You can use LINSPACE to generate evenly spaced trial numbers, or you can us 1 + rand(1,n) to generate n random numbers between 1 and 2. Then you can check the condition using MATLAB's elementwise array operators: bool = x.*(1./x) ~= 1. Notice the .* instead of *, since * without the . is matrix multiplication. Same thing for division. Actually if you generate a boolean array that way from a set of trial numbers, you can also extract the results from your trial vector x using MATLAB's logical indexing, e.g. x(bool). Try it!

Answer 2

[Walter Roberson]

Do a binary search over the interval realmin() to 1, to find the boundary point.