I guess you got this from some math software? Then it may refer to the fact that what we are used to write as 2 = 2 ( 2 equals 2) in this software has to be written as 2 == 2 (in Mathematica there is even a === relation). For such software the single = means asignment, which is not a relation.

BTW, it would help if you could state your problem a bit clearer.

No condition is required

Unless 2 is 3 ;)

Under no other condition other than that the sign "=" means equality.

if they have same signs

I guess you got this from some math software? Then it may refer to the fact that what we are used to write as 2 = 2 ( 2 equals 2) in this software has to be written as 2 == 2 (in Mathematica there is even a === relation). For such software the single = means asignment, which is not a relation.

BTW, it would help if you could state your problem a bit clearer.

2 = 2 is a tautology, that is, a particular case of X = X. As every tautology there is no information in it. Nevertheless, I guess that the author of this thread is testing the sense of humor of contributors and their simplemindedness. I can answer the question as it is "deserved":

The equality 2 = 2 is only true for small values of 2.

Following Prof. Juan-Esteban post, this is my deserved answer:

2=2 under the same condition X=X.

Dear Janamejay,

can we hope to get your solution of the puzzle you gave us?

Since much of my work (also that of Albert E.) is based on the hope that 2 turns out to equal 2, I'm very much interested to know the precise conditions for this hope to become true.

What kind of a question is that ?

By definition is all there ever is to it.

Helo, Janamejay,

Can you give us some more information about your question?

Depending on what we're talking about, although it seems to be a obvious statement, 2 = 2 is restricted to some conditions, indeed.

If you are talking about programming, then the equals sign you are using must mean equality, because in most (if not all) languages, you are not allowed to name a variable with a numeric character. In this case, depending on how the system represents your "2" (e.g. character, string, integer, short, floating point, double precision, etc), then this statement would lead to "false".

However, if we are talking about Mathematics, more specifically the most usual representation of Mathematics, then we are comparing two scalar values and there is no reason why this statement would be false. Although I wonder if one could write 2:=2 instead of simply 2=2.

Still talking about Mathematics, if you are working with limits, the use of the equality turns out to be confusing. Take the example of the following function:

lim (sin(2x))/x = 2

x->0

We know that this limit leads to two. However, we cannot replace x=0 on the actual function, because it is undefined for this value. This fact turns out to be confunsing for some people.

These are the ideas that came to my mind when I read your question, but I still need more information to give a clearer answer...

for that 2 has to be equal to 2

I am impressed. I cannot understand how a simple question can induce such a lot of answers leading to no aim. In spite of the funny underlying intention in the question, I try to analyze it seriously.

A condition in order to be true the expression 2 = 2, must consist of attributes of the symbols in this expression. This expression is true, provided that the first occurrence of the symbol 2 has the same meaning as the second occurrence. This circumstance occurs whenever the used language is not positional.

For instance consider the following sentences;

1) This man constructs fast vehicles.

2) This man constructs vehicles fast.

Both sentences consist of the same words, but in different ordering; however they have different meanings because English is a positional language, that is, order sensitive. Accordingly, the condition to be true the expression 2 = 2 is:

>.

2=2 under the condition that condition=condition, which in modulus arithmetic is not so tautological.