MATLAB: I have this code which is behaving differently for decimal and integer values. Where am I missing?

Question

 x=0.1;
 y=0.1;
 a=[x,y];
 b=[0.2,0.2];
 tf=isequal(a,b);
 while tf==0
     x=x+(0.01);
     y=y+(0.01);
     a=[x,y];
     tf=isequal(a,b);
 end
 disp(a);

if i replace the x, y and incremental values by integers, it works !! for ex as shown below

x=1000;
y=1000;
a=[x,y];
b=[2000,2000];
 tf=isequal(a,b);
 while tf==0
     x=x+1;
     y=y+1;
     a=[x,y];
     tf=isequal(a,b);
 end
 disp(a);

Answer 1

"That is really weird indeed. Perhaps MATLAB struggles to determine equality for floating point numbers"

Not at all: if two numbers are really equal, then MATLAB will correctly identify them as such. The only struggle here is beginners who believe that 0.1 is really stored in their computer, and have yet to learn that floating point number errors accumulate through all computations. Which means that those numbers are NOT equal.

"Where am I missing??"

Never use == to test for equivalence of decimal values. Always compare the difference against a tolerance:

abs(A-B)<tol

You need to learn about the practical limits of floating point numbers:

http://www.mathworks.com/help/matlab/matlab_prog/floating-point-numbers.html

http://www.mathworks.com/matlabcentral/answers/69-why-does-1-2-3-1-3-not-equal-zero

http://matlab.wikia.com/wiki/FAQ#Why_is_0.3_-_0.2_-_0.1_.28or_similar.29_not_equal_to_zero.3F

http://www.mathworks.com/matlabcentral/answers/57444-faq-why-is-0-3-0-2-0-1-not-equal-to-zero

http://www.mathworks.com/company/newsletters/news_notes/pdf/Fall96Cleve.pdf

http://www.mathworks.com/matlabcentral/answers/41536-why-is-2-24-10-22-4-not-equal-to-0

https://www.mathworks.com/matlabcentral/newsreader/view_thread/66553

http://blogs.mathworks.com/loren/2006/08/23/a-glimpse-into-floating-point-accuracy/

http://www.mathworks.com/help/fixedpoint/ug/floating-point-numbers.html

And some external links on this topic:

http://www.lahey.com/float.htm

http://matlabgeeks.com/tips-tutorials/floating-point-comparisons-in-matlab/

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

The solution is always the same, as shown in all of those links: compare the absolute difference against a tolerance, like this:

abs(A-B)<tol

Methods to be avoided: converting to string is very slow, and rounding the values introduces artifacts that do not exist in the data.