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Integers and Real Numbers

Draw the real line and label from about -5 to 5 in increments of 1. There are an infinite amount of integers on the real line. Based on your sketch you'll also agree with me that there are twice as many total integers as there are positive integers, right? But how many positive integers are there? That's it... an infinite amount. So there are infinite amounts of integers both on the entire real line and on each half of the real line. Are you scratching your head yet?

Now consider the real numbers. In fact, lets narrow our focus way down to just the part of the real line between 0 and 1. Circle that part of the real line. How many real numbers are there in between 0 and 1? What can you conclude from all this?

Solution Preview

Hi, your idea is absolutely right.

On the real number line there are infinite number positive and negative integers.

Now consider the real numbers on a number line.

Take part of the line between 0 and 1.

The question is how many real numbers are there in between 0 and 1.

There are infinite amounts of ...

Solution Summary

Integers and real numbers are discussed.