this page was updated last 11 October 2000


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YOUR ANSWER: Any number is equal to itself.

You are correct. The english sentence "Any number is equal to itself" expresses exactly the idea that our table of specific numbers illustrates . In the present case, then, we can make our general statement about numbers in words, although we had to use six words about numbers. Let's see if we can do better with symbols.

Let us define a symbol. We will say that the symbol n will mean "any number." That is all we will say about our symbol n at this time. We simply mean that wherever we use the symbol n it stands for any number. Now we will write a statement using our new symbol in accordance with its prescribed definition. The statement is:

n = n.

Now, bearing in mind the definition we have given for our symbol n, and also that mathematicians are a crabby and cantankerous lot when dealing with definitions, what does our statement n = n say?