MATLAB: Matlab equality problem. Please help.

==cossin

Hi, this is my code.
theta(k) = 45
l = x.*cosd(theta(k))+y.*sind(theta(k));
l(1,1) == l(3,3);
x(1,1)*cosd(45)+ y(1,1)*sind(45) == x(3,3)*cosd(45)+ y(3,3)*sind(45);
x(1,1)+ y(1,1)==x(3,3)+ y(3,3);
However, matlab it saying
l(1,1) == l(3,3)
is false,
x(1,1)*cosd(45)+ y(1,1)*sind(45) == x(3,3)*cosd(45)+ y(3,3)*sind(45)
is false, and
x(1,1)+ y(1,1)==x(3,3)+ y(3,3)
is true. I am wondering why because I believe l(1,1) == l(3,3) is true.

Best Answer

You have to learn about floating point numbers, and why you should not test them for equality like that. Always compare the absolute difference against a tolerance, like this:
abs(A-B)<tol
Start by reading these:
https://www.mathworks.com/matlabcentral/answers/57444-faq-why-is-0-3-0-2-0-1-not-equal-to-zero
https://www.mathworks.com/matlabcentral/answers/316889-why-two-equal-numbers-are-not-equal
http://www.mathworks.com/matlabcentral/answers/102419-how-do-i-determine-if-the-error-in-my-answer-is-the-result-of-round-off-error-or-a-bug
http://www.mathworks.com/matlabcentral/answers/140656-about-numerical-difficulty-of-equality-comparison-operation-between-two-double-real-numbers-in-matlab
This is worth reading as well:
https://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html
http://faculty.tarleton.edu/agapie/documents/cs_343_arch/papers/1991_Goldberg_FloatingPoint.pdf
To see the "real" value download James Tursa's FEX submission:
https://www.mathworks.com/matlabcentral/fileexchange/22239-num2strexact-exact-version-of-num2str
"I am wondering why because I believe l(1,1) == l(3,3) is true"
If you use num2strExact on both of those values, you will find that they are not the same, and MATLAB's output is correct. That is why you should compare the absolute difference against a tolerance.
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