Part 7, Chapter 1, Algebra 1

Service Description

The book goes on with the conversation about using letters for items in problems of math. " Recordis had another objection. "There aren't nearly enough letters," he said. "There are only 26 letters, so after we have used all 26 of them, we will be absolutely stuck." "We can use a letter more than once!" the professor exclaimed. "For example, if we use the letter h to stand for hours today, there is no reason why we can't use the letter h to stand for something else, such as height, tomorrow." "But how will we tell which one it means?" Recordis asked. "We will have to tell from the context--in other words, we will have to know what problem we are working," the king said. "And we will have to make sure that we don't use the same letter to stand for two different things in the same problem. But there is no reason why we can't use a letter to stand for one thing when we are working on one problem and another thing when we are working on a different problem." "I personally know four people named John," the professor said. "And that usually doesn't present a problem--just so long as I make clear at the beginning of a conversation which particular John I happen to be talking about at the moment." Recordis was still grumbling to himself, but since he could not think of any more objections at the moment, the king went on to explain some more advantages of using letters to stand for numbers. (A letter that stands for a number is often called a 'variable.) "We can write the commutative (order-doesn't-make-a-difference property) of addition in a much shorter fashion," the king said. "Let's use the letter a to represent one number and the letter b to represent another number. Then we can say that a + b=b + a for any values of a and b." "Now we have a very useful tool that can allow us to develop lots of general results!" the professor said excitedly. (Grandma will continue the story or chapter in another part.)