Unknown x: x+1=1 in machine numbers

How do I set unknown variable x to find the largest x for which x + 1 = 1 in Matlab?

[José-Luis]

   eps(1)

[JIM]

Yeah but if I want the smaller x for whick x=x+1? Is the same? And the largest x is the eps(y) for every y for which x+y=y?

Thank you for your answer!

Answer 1

[Matt Fig]

x = eps(1)/2;

If x is larger than this, 1+x>1.

[JIM]

So..

x=eps(1)
while x+1>1;
x=x/2;
end

And I found the x?

EDITED by Matt Fig.... simply highlight the code and press the {} Code button...

[Matt Fig]

Oh, you didn't say you were trying to get to this number by calculation! Sure:

x = 1;
while x+1>1
  x = x/2;
end

[JIM]

OK..Therefore:

x=y;
while x+y>y;
x=x/2;
end

for every y?

And for the smaller x for which

x+9999=x

which x we put on original value? (

 while x+9999<x;
   x=x/2;?

)

[Matt Fig]

Dude, please take the time to use the {} Code button!

[JIM]

Sorry..

[Matt Fig]

Naw, that won't get it. You will have to zoom in on it once you find the x such that x/2+y is not greater than y.

[JIM]

Do you mean:

x=y;
while x+y<y;
x=x/2;
end

This is not correct

[JIM]

I think that the correct code for the largest x is this:

x=5000;
while x+5000>5000;
x=x/2;
end

Right?

[Matt Fig]

What do you mean "the largest x"? That code returns a number that is not the largest x one can add to 5000 such that: (x+5000)==5000

The largest number x one can add to any y such that

(x+y)==y  % is x=eps(y)/2

So this is how you check your code..

[JIM]

I mean the largest number x that recognized by "my" computer for which x+5000=x (so the x is a very small number and I try to find this small number)

[Matt Fig]

Like I said, you will get close with the code I gave you above, then you can zoom in by looking at smaller differences than x/2. Is this homework?