Topics: Infinity, Length, Real number Pages: 3 (834 words) Published: October 8, 1999

There is only one being, continuous, material, and motionless.

Let's take a moment to examine a number line.

5 10 15 20 25 30 35 40 45 50 55 60 65 70

It's pretty simple to understand. The line represents a distance, and the "|" characters symbolize different points on the line-the exact points are differentiated by the number below them.

Any number line is understood to have contain points which aren't necessarily designated by a number. For example, on the above number line we know that between 5 and 10 we can find the point 7. This example is illustrated below.

5 7 10

In fact, it is understood that there are an infinite number of points on any number line. Between 5 and 7 we can find the points 5.009852, 5.9, 6, 6.262623627000029873257690125762, 6.3336, 6.999, 6.9999, etc.

Rulers are examples of how we might commonly use a number line. Different rulers mark off different distances such as yards, feet, inches, centimeters, millimeters, and so on. Obviously rulers cannot be used to measure all distances because some distances may be too small to be measured practically with the naked eye.

Hypothetically speaking, let's say you had a worm and a razor blade. Let's also hypothesize that this particular worm is two inches long. Now if you were to cut this worm exactly in half you should have "two worms" each one inch long.

If you then took one of those one inch pieces and cut it in half you would then have two pieces each one fourth of an inch long-I don't really know how many times you can cut a worm in half before it stops becoming two worms and just becomes pieces of worm.

Theoretically, if you had the right tools, you should be able to continue cutting that worm in half forever. You simply take one of those 1/4 inch pieces, cut it, and...
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