No, there is no odd natural number divisible by 2.
Understanding Odd and Even Numbers
To understand why no odd natural number is divisible by 2, let’s define what we mean by odd and even numbers:
- Even Numbers: These are integers that are exactly divisible by 2, leaving no remainder. Examples include 2, 4, 6, 8, and so on.
- Odd Numbers: These are integers that, when divided by 2, leave a remainder of 1. Examples include 1, 3, 5, 7, and so on.
Why No Odd Number Is Divisible By 2
The key point to remember is that divisibility by 2 is the defining characteristic of even numbers. By definition, odd numbers are those that cannot be divided evenly by 2.
Here's a table summarizing the key differences:
| Number Type | Divisible by 2? | Remainder When Divided by 2 |
|---|---|---|
| Even | Yes | 0 |
| Odd | No | 1 |
Reference Information
As the provided reference states, "Set of odd natural numbers divisible by 2 is an example of a null set. The null set defines the set which has no element in it. There exists no odd natural number which is divisible by 2". This reinforces the concept that no odd number can ever meet the criteria of being divisible by 2.
Practical Insight
You can think of odd numbers as being "one more" than an even number. Every even number can be paired up perfectly into groups of two. An odd number, however, always has a single unpaired element, ensuring that it can not be divided exactly by 2.
Conclusion
In summary, the statement that odd natural numbers are divisible by 2 is a contradiction. This is because the definitions of 'odd' and 'divisible by 2' are mutually exclusive.
