Which of the following is NOT true with reference to a real number?

Options

A. All irrational numbers are real numbers
B. A real number need not necessarily be a point on the number line
C. A Real number is unique
D. All rational numbers are real numbers

Answer

To determine which statement is NOT true with reference to a real number, we will analyze each option provided.

1. **All irrational numbers are real numbers.**
- This statement is true. Irrational numbers, such as √2 or π, are indeed part of the real number system.

2. **A real number need not necessarily be a point on the number line.**
- This statement is NOT true. By definition, real numbers correspond to points on the number line. Therefore, every real number must be represented as a point on the number line.

3. **A real number is unique.**
- This statement is true. Each real number is distinct and can be represented uniquely on the number line.

4. **All rational numbers are real numbers.**
- This statement is also true. Rational numbers, which can be expressed as a fraction of two integers, are included in the set of real numbers.

Based on the analysis above, the statement that is NOT true is:

**Answer: A real number need not necessarily be a point on the number line.**

### Step-by-Step Solution:

1. **Identify the statements regarding real numbers.**
- List the options given in the question.

2. **Evaluate each statement for its truth value.**
- Check if each statement aligns with the definition of real numbers.

3. **Determine which statement is false.**
- Compare the statements against the known properties of real numbers.

4. **Conclude with the correct answer.**
- Identify the statement that does not hold true.