By Garrett Birkhoff

This vintage, written through younger teachers who grew to become giants of their box, has formed the certainty of contemporary algebra for generations of mathematicians and is still a important reference and textual content for self learn and faculty classes.

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Now we can be more explicit, since we have previously defined the word multinomial. The only part of the definition of a term given in review item 23 that may seem new to you is that the sign is a part of the term—and an important part. In Unit 2, we will discuss the fact that (+) and (-) symbols can be used either as signs of operation (that is, telling us to add or subtract quantities) or as indications that the quantities themselves are positive or negative. Although we will not go into this in any detail now, the example shown illustrates this idea.

The answer is "2. Now let us consider how to subtract a negative number from a positive one. You have seen one example of this. Here is another. To subtract "3 from +5, count from "3 to +5. The distance is 8 and the direction is upward (positive). The difference, therefore, is +8, as shown on the vertical scale below. Remember: Always count from the subtrahend to the minuend. This determines the direction in which you are counting and therefore the sign of the answer. Write out below, in a horizontal line, the algebraic solution to the subtraction performed above.

Of two 6. The diagram above represents all the elements of the real number system and, therefore, all the numbers with which we will be concerned. In order to be able to refer to positive and negative numbers properly, we call them signed numbers. Although zero is neither positive nor negative, we include it with the signed numbers. You already are familiar with several kinds of signed numbers. A thermometer, for example, has a scale containing both positive numbers (numbers above zero) and negative numbers (numbers below zero).