Question

I was under the impression that = is an assignment, == is a numeric comparison, and === is a symbolic comparison (as well as in some other languages == being equal to and === being identical to. However, looking at the following it would appear that this is not necessarily the case…

In: x == x
Out: True

In: x === x
Out: True

In: 5 == 5
Out: True

In: 5 === 5
Out: True

In: x = 5
Out: 5

In: 5 == x
Out: True

In: 5 === x
Out: True

In: 5 5 == 5x
Out: True

In: 5 5 === 5x
Out: True

In: x == y
Out: x == y

In: x === y
Out: False

In: y = x
Out: 5

In: x == y
Out: True

In: x === y
Out: True

So what exactly is the difference between == and === in Mathematica? I have been looking at the documentation but I still don’t quite understand it.

Answer 1

One important difference is that === always returns True or False. == can return unevaluated (which is why it’s useful for representing equations.)

In[7]:= y == x^2 + 1

Out[7]= y == 1 + x^2

In[8]:= y === x^2 + 1

Out[8]= False

There are some interesting cases where == returns unevaluated that are worth being aware of while programming. For example:

In[10]:= {} == 1

Out[10]= {} == 1 

which can affect things like If[foo=={}, <true>, <false>].