Why does 2+2=4?

Solution
2+2=4 is an equation by the simple fact of your admission and supposition that these two terms in question (technically, 2+2 is an expression but a term nonetheless) are subject to the laws of algebraic logic that terms can only be separated by a symbol to suggest equality, non-equality and/or otherwise.

Since 2+2 is neither less than 4, greater than 4 or unequal to 4 it is equal to 4 by the most simplest of algebraic logic, however...

2+2 is not greater than or equal to 4 for the same reason that 2+2 is not less than or equal to 4. Algebra requires that all expressions be reduced to absolutes when no variables are present when attempting to solve. Since: 2+2=4 has no variables; you simply take the left hand of the equation and...

Pyrmon

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Numbers are a graphic representation on a fixed amount of unities.
1 represents a single unity while 2 represent two of them.
4 represents four unities.
So two unities joined by another pair of unities equals four unities. It is a equilibrium.
It just means that both of them are different ways of representing the same thing. The same way that two paths can get you at the same place. One longer, the other shorter. You just usually take the shorter one because it's... well... shorter.
 

Nathan Drake

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Enjoy a stupidly long explanation that I copy pasta'd from a Google answers thing.

"I hope you like this brief answer to what is actually an incredibly
complex question.

The simple answer is that, in everyday mathematics, in number base
systems higher than ?4,? 2 + 2 = 4 because it is defined as such.
Based on the definitions of the number ?2?, the number ?4?, and the
mathematical operation of addition, the answer is always the same. It
is at the basis of all number theory and other branches of
mathematics.

Simply put, if you take a pile of objects that we designate as
consisting of ?2? objects, and place it with another identical pile,
the count of the resulting pile of objects is equal to what we label
as the number ?4.?

Of course, there are other number systems and other ways of doing math
where that definition is not used, but they don?t generally produce
very useful results for everyday applications.

You can find a longer explanation at:
http://www.mathmojo.com/interestinglessons/why%20do2plus2equal4/why%20do2plus2equal4.html,
but it says generally the same thing.

It may surprise you to learn that an entire book, Principia
Mathematica, (the one by Whitehead and Russell, 1910-1913, not the one
by Sir Isaac Newton in 1687) devotes several hundred pages to deriving
an explanation of just why 2 + 2 = 4 (actually, as I recall, it was 1
+ 1 = 2).

I don?t recommend that you pick up a copy of this 2,000-page,
three-volume set, since it consists almost entirely of equations.

You can find some excellent discussions about the nature of
mathematical proofs and in particular some 3,000 logic and set theory
proofs at:
http://us.metamath.org/mpegif/mmset.html

In particular, you can find links to a 122-level ?proof? of why 2 + 2 = 4 at:
http://us.metamath.org/mpegif/mmset.html#trivia

A complete proof, such as the one presented in Principia Mathematica,
involves 1,789 sub-theorems consisting of 19,731 individual steps.

As some others have already commented, the question about quantum
mechanics only applies to extremely small events at and below the
atomic level. The mathematics involved in solving questions in quantum
mechanics seldom even involves addition. In the simplest sense, as I
once heard an old friend, John Van Vleck, Nobel Laureate Physics,
1977, say, you should always think of any question involving quantum
mechanics as being a question of probabilities. In that sense, in
quantum mechanics 2 + 2 never = 4 with any certainty.

You will find a more extensive, but still reasonably accessible,
introduction to quantum mechanics and mathematics at:
http://www.math.rutgers.edu/~oldstein/quote.html

One thing to keep in mind is that when you start getting into the
details of advanced physics then you must switch languages. The reason
things don?t seem to make sense at the atomic and sub-atomic levels is
that non-physicists are forced to discuss things in English or some
other language, which leads to what appear to be contradictions. In
reality, you can only discuss such things in mathematics, which is why
you will find most scientists very reluctant to talk about their work
with non-scientists.

Think about it this way. You would never use chemistry notation to
show someone how to bake a cake. In the same way, you simply can?t
explain most advanced physics concepts in English or any spoken
language; the best you can do is summarize, simplify, and generalize ?
the language simply won?t support detailed explanations without
resulting in apparent paradoxes or contradictions."

www.google.com
 

Snailface

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Because somebody a long time ago decided 2+2=4 and a bunch of people since then have decided to believe it as well without argument. Really, if you want, you don't have to accept this as truth. You could redefine, in your mind, the meaning of these numbers. For example 2 = goat and 4 = fish and then the question no longer makes sense. There is no law that states an abstract man-made concept has to be true or definable. Believe it or not, that is your choice.
 

mechadylan

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2+2=4 is an equation by the simple fact of your admission and supposition that these two terms in question (technically, 2+2 is an expression but a term nonetheless) are subject to the laws of algebraic logic that terms can only be separated by a symbol to suggest equality, non-equality and/or otherwise.

Since 2+2 is neither less than 4, greater than 4 or unequal to 4 it is equal to 4 by the most simplest of algebraic logic, however...

2+2 is not greater than or equal to 4 for the same reason that 2+2 is not less than or equal to 4. Algebra requires that all expressions be reduced to absolutes when no variables are present when attempting to solve. Since: 2+2=4 has no variables; you simply take the left hand of the equation and... ... oh shit, I see what you mean. Nm.
 
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