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Q: This is a line representing the set of all real numbers?

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All real numbers.

All real numbers.

Yes, because all numbers on the number line are real numbers

the set of real numbers

That would be the real numbers.

Irrational numbers are real numbers because they are part of the number line.

The set of all real numbers usually represented by a capital R that is double vertical line in the left and bold.

Yes. Traditionally, this line is drawn horizontally, with positive numbers to the right, and negative numbers to the left.

When we investigate the real numbers, we often use the concept of the real number line. This line will have a distinct point on it for each real number, and will divided by the number zero. To the right of zero, we'll have the positive real numbers, while on the left of zero, we'll find the negative real numbers. The line will extend to infinity in each direction. These are the foundations for the study of the real numbers. All we need now is the unit length which will allow us to locate the number 1 on the real number line. From there, we're off and running; we can locate any other number we care to find. They're all on the line.

The number 4.83 is a real number. Real numbers include all whole numbers, fractions, and decimals that can be represented as quantities along a continuous line.

5

All natural numbers are also real numbers, but all real numbers are not necessarily natural numbers because natural numbers are positive whole numbers. Real numbers are any number on the number line, which includes irrational numbers like pi and sqrt2. Thus only the positive natural numbers are both natural and real. Hope this is not too long-winded!

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