Equations
"Defining Variables" discussed assignments such as 
which set x equal to y. Here we discuss equations, which test equality. The equation 
tests whether x is equal to y.
This
tests whether
and
are equal. The result is the symbol
True.
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It is very important that you do not confuse 
with 
. While 
is an imperative statement that actually causes an assignment to be done, 
merely tests whether x and y are equal, and causes no explicit action. If you have used the C programming language, you will recognize that the notation for assignment and testing in Mathematica is the same as in C.
| x=y | assigns x to have value y |
| x==y | tests whether x and y are equal |
Assignments and tests.
This
assigns 
to have value
.
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If you ask for
, you now get
.
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This
tests whether
is equal to
. In this case, it is.
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This removes the value assigned to
.
The tests we have used so far involve only numbers, and always give a definite answer, either True or False. You can also do tests on symbolic expressions.
Mathematica cannot get a definite result for this test unless you give
a specific numerical value.
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If you replace
by the specific numerical value
, the test gives
False.
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Even when you do tests on symbolic expressions, there are some cases where you can get definite results. An important one is when you test the equality of two expressions that are identical. Whatever the numerical values of the variables in these expressions may be, Mathematica knows that the expressions must always be equal.
The two expressions are
identical, so the result is
True, whatever the value of
may be.
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Mathematica does not try to tell whether these expressions are equal. In this case, using
Expand would make them have the same form.
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Expressions like 
represent equations in Mathematica. There are many functions in Mathematica for manipulating and solving equations.
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You can assign a name to the equation.
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If you ask for
, you now get the equation.
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