Algebra Know-It-ALL

Are you confused? If the toothpick numeral system puzzles you, don’t feel bad. It’s awkward. It’s impractical for expressing gig ...

Roman Numerals The toothpick numeration system just described bears a resemblance to another system that was actually used in mu ...

and dividing, it’s almost impossible to get along without zero. In a computer, the numeral 0 is one of only two possible digits ...

Hindu-Arabic Numerals The numeration system we use today was invented in the seventh century by mathematicians in Southern Asia. ...

seven hundred eight thousand sixty-five. (Some people would call it seven hundred and eight thousandand sixty-five.) It’s custom ...

Another interesting property of the Arabic system is the fact that there is no limit to how large a numeral you can represent. E ...

The Counting Base Theradix or base of a numeration system is the number of single-digit symbols it has. The radix-ten system, al ...

After the first revolution, you keep the V and then start adding symbols to its right: VI, VII, VIII. But when you get past VIII ...

see this notation often in mathematics.) Continuing through the second revolution and into the third, you count ... 15, 16, 17, ...

The binary system When engineers began to design electronic calculators and computers in the twentieth century, they wanted a wa ...

converts the result back to a decimal numeral, and then displays that numeral for you. All of the conversions and calculations, ...

16 Counting Methods Table 1-2. The conventional (or decimal) numerals 0 through 64, along with their binary, octal, and hexadeci ...

Practice Exercises 17 Table 1-2. The conventional (or decimal) numerals 0 through 64, along with their binary, octal, and hexade ...

Convert the following Roman numerals to decimal numerals. (a) MMXX (b) MMXIX (c) MMIX (d) MMVI Write down the number three hund ...

Before going farther with numbers, you should be familiar with sets and the symbols that describe their behavior. Sets are impor ...

Listing the elements When the elements of a set are listed, the list is enclosed in “curly brackets,” usually called braces. The ...

elements,” and you’ve named all the elements of the null set. When a set is infinite, you can’t name all of its elements, no mat ...

Are you confused? Do you still wonder what makes a bunch of things a set? If you have a basket full of apples and you call it a ...

large, heavy rectangle represents the set of all things that can exist, whether real or imaginary (and that includes all possibl ...

Figure 2-1 shows that the set of all the women in Chicago is a subset of the set of all the people in Illinois. That is expresse ...