Time Machine

College and School of Mathematics
Math::Arithmetic::Grade II::Playing with Numbers

You can play with numbers in many ways. Two ways you can play is to use two of the properties of numbers. They are Commutative Property and Associative Property. Here's how it works.

Commutative Property comes from the word "commute" like "I commute to school by bus." So watch how I commute the number 1 in the following example.

1 + 2 can be written in another way. The number 1 can commute to the other side of 2. So we can write it like this:

2 + 1

This also works when you're multiplying as follows with the numbers 3 and 4:

3 x 4 can be written as 4 x 3.

Associative Property of numbers comes from the word "associate" like "He's my associate. He's my friend."  In math, we use a pair of parentheses to associate two numbers together. So watch how I associate the numbers 5 and 6 below.

5 + 6 + 7 can use the associative property of numbers so we can write these numbers as:

(5 + 6) + 7

Let's say the number 6 likes to associate with number 7 instead, so we can write it as follows:

5 + (6 + 7)

By the way, associative property also works when you're multiplying.

Now, it's your turn to play with numbers. Use the commutative property in the following numbers:
a.  3 + 4
b.  5 x 6
c.  7 + 8
Now use the associative property with the following numbers:
d.  9 + 10 + 11
e.  12 x 13 x 14
f.  15 + 16 + 17

Let's party with numbers!

John Sindayen

Math::Intermediate Algebra::College Freshman::Functions

The concept of calculus revolves around functions. A function is a relation but a special kind of relation.

What exactly is a function? Function relates two sets of numbers in such a way that when an element of the first set is used in the function, the function returns one and only one element from the other set. Mathematically speaking, let's say we have a function called f, the first set of numbers called x, and the second set of numbers called y, so then we can write the following:

f(x) = y, where for every x value there is only one y value.

Let's take for example the movement of a clock. The minute hand goes around and around in the same pivot point, therefore, it's movement is not a function. Why? Because where x = 0 (the pivot point), y can be either 12 or 6.

Most people think of time as a function, however. Time can be a function if time does not become negative, that is if time does not go backwards in time. Therefore, to create a time machine that goes backwards in time, one should not use calculus for computation.

Now, it's your turn to write or draw some functions using the Cartesian Coordinate System. Write or draw 5 relations that are functions.

Read how Jules Verne invented "The Time Machine"!

John Sindayen

Math References:
http://www.thefreedictionary.com/calculus
http://mathonweb.com/help_ebook/html/functions_6.htm
http://www.imdb.com/title/tt0268695/