Why is NaN not equal to NaN

Why is this not true?

NaN==NaN

ans =

     0

Answer 1

[Cedric]

Most times, you don't want this test to return true indeed. Imagine testing a==b and having a true result when both a and b are undefined; this would make little sense. It is the same with NaN.

While it is not the original question, note that you can test equality assuming NaN 's are equal:

http://www.mathworks.com/help/matlab/ref/isequalwithequalnans.html

But with that you usually want to test if "behaviors" are the same (and not equality per se), e.g. if two functions return the same number or both NaN do something, else do something else.

[Matt J]

Although more recently, isequalwithequalnans has been deprecated in favor of isequaln

http://www.mathworks.com/help/matlab/ref/isequaln.html

[Cedric]

Ah thank you, I still have 2011b and I wasn't aware (despite linking the doc for 2012b ;-/).

Answer 2

[Matt J]

Because equality is a notion applied to numbers. How can 2 things be equal when they are not numbers?

[Walter Roberson]

Not true. For example, 'A' == 'A', and equality of data structures can be defined.

The answer is simply "By Definition". http://en.wikipedia.org/wiki/NaN

A comparison with a NaN always returns an unordered result even when comparing with itself.

[Matt J]

I would argue, though, that 'A' could be considered a number.

I would also argue that the definition that you cite is motivated precisely by the fact that NaN is not to be considered a number and therefore not meant to have inter-comparison operations that numbers typically have.

[Cedric]

I would argue that 'A'=='A' is testing actually numerical equality of ascii codes, hence numbers.

To illustrate

 >> 'A'==65
 ans = 1

Or let say that I have the impression that each time my lhs/rhs could not be directly typecast-ed into numbers, I had to use a more elaborate test, like isequal().

[Walter Roberson]

Cedric: MATLAB does not use ASCII. If it did, it would not be possible to use any codepoint above 127. MATLAB uses a custom 16 bit coding that is the same as UTF-16-BE up until (I think it is) 0xBFFF (from 0xC000 onward signals additional bytes in UTF-16 but not in MATLAB's coding.)

MATLAB's == operator (eq) is defines specifically with

eq(A, B) is called for the syntax A == B when either A or B is an object.

thus allowing for the possibility of comparison being held equal when the numeric representations are not identical.

Matt: NaN could, I think, have been defined as comparing equal to itself, and I don't think much would have changed, except for the question of whether various NaN are equal to each other. (NaN is not a single value: there are something like 2^50 different Quiet NaN, and the same number of Signalling NaN; the NaN issued was intended to reflect the reason the NaN was generated, such as inf - inf giving a different NaN than inf * 0 -- so you would still want to be using isnan() rather than comparing to a particular NaN.)

[Cedric]

Thank you for your comment, Walter. I meant ASCII having extended ASCII in mind (8bits), and I never realized that it was 16 bits UTF-like indeed!

[math man]

You might wonder, though, why NaN ~= NaN returns true?

That is, if they are not numbers why are they compared in this case to give a misleading result?

[Matt J]

@math man So you think the result of NaN ~= NaN should be NaN? Maybe.