g = 0.1;x = 0.102;x = x - 0.001;x = x - 0.001;x == gThis is a simple code and I didn't know why matlab give me logic 0 for compare x==g
ans = logical 0MATLAB: This x == g gave me logic 0
comparelogic
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"Problem with Less than or Equal to Operator"
Nope, there is no problem with the eq operator. All you have discovered is that two different binary floating point numbers are different, and that you should never test for equality of binary floating point numbers.
Always compare the difference of floating point numbers against a tolerance:
abs(A-B)<=tol"How come this is possible?"
The value that you are trying to compare cannot be exactly represented using binary floating point numbers. What you see printed in the command window is the closest representation to 5 or 16 significant digits, depending on your current format setting. To see the "real" value download James Tursa's FEX submission:
Use James Tursa's num2strexact and you will see that none of those values really have the exact value 0.001. All you are looking at is a representation of those floating point numbers displayed in the command window, to the precision defined by your format setting. Just because you see 0.001 is displayed tells you nothing about the "real" floating point number's value.
You need to learn about the limits of floating point numbers. Start by reading these:
This is worth reading as well:
"...but Matlab still says they aren't equal?"
Because they aren't equal.
This is very easy to check (you already used one method, here is another):
>> r1Xf - r2Xfans = -8.8818e-016 4.4409e-016 0>> x - r1Xfans = 0 -1.1102e-016 0>> x - r2Xfans = -8.8818e-016 3.3307e-016 0"... the cross products should be equal "
Nope, I don't see any reason to expect them to be equal. Operations on floating point numbers collect floating point error. You need to learn about the limits of floating point arithmetic.
"I don't understand why the arrays are all [-2.2, -0.4, 1.0]..."
Because the operations collect different floating point error for different input values. What you see printed in the command window is the closest representation to 5 or 16 significant digits, depending on your current format setting. To see the "real" value download James Tursa's FEX submission:
Use James Tursa's num2strexact and you will see that none of those values really have the exact value -2.2 or -0.4. All you are looking at is a representation of those floating point numbers displayed in the command window, to the precision defined by your format setting. Just because you see -2.2 or -0.4 displayed tells you nothing about the "real" floating point number's value.
You need to learn about the limits of floating point numbers. Start by reading these:
This is worth reading as well:
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