Category theory at work by H. Herrlich, H-.E. Porst, M. Erne

By H. Herrlich, H-.E. Porst, M. Erne

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Both the universal set and the empty set are subsets of every set. Describing sets Rule is a method of naming a set by describing its elements. {x:x > 3, x is a whole number} describes the set with elements 4, 5, 6,…. Therefore, {x:x > 3, x is a whole number} is the same as {4,5,6,…}. {x:x > 3} describes all numbers greater than 3. This set of numbers cannot be represented as a list and is represented using a number line graph, which is discussed in Chapter 8. Roster is a method of naming a set by listing its members.

Example 29: Express the following in scientific notation. 1 × 10 6. Simply place the decimal point to get a number between 1 and 10 and then count the digits to the right of the decimal to get the power of 10. 100000. 0 × 10–7. Simply place the decimal point to get a number between 1 and 10 and then count the digits from the original decimal point to the new one. 0000004. moved 7 digits to the right Notice that number values greater than 1 have positive exponents as the power of 10 and that number values between 0 and 1 have negative exponents as the power of 10.

Therefore, using the same rule as in subtraction of signed numbers, simply change every sign within the parentheses to its opposite and then add. Example 6: Subtract the following. (a) 9 –(+3 – 5 + 7 – 6) = 9 + (– 3 + 5 – 7 + 6) = 9 + (+1) = 10 (b) 20 – (+35 – 50 + 100) = 20 + (–35 + 50 – 100) = 20 + (–85) = –65 Multiplying and dividing signed numbers To multiply or divide signed numbers, treat them just like regular numbers but remember this rule: An odd number of negative signs will produce a negative answer.

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