# How to prove that it does not exist a natural number having the

• Mark J.
In summary, there is no natural number that can be multiplied by 5 through a permutation of its digits. This was clarified to mean that one number is 5 times the size of the other.
Mark J.
How to prove that it does not exist a natural number having the property that the permutation of the first digit with the last one produces a new number being 5 times bigger compared to the original one

Regards

Mark J. said:
How to prove that it does not exist a natural number having the property that the permutation of the first digit with the last one produces a new number being 5 times bigger compared to the original one

Regards

Does "5 times bigger" mean that one number is 5 times the size of the other, or does it mean that one is 6 times the other (so the amount by which is is bigger is 5 times)?

RGV

no problem just figured it out.
thx

Mark J. said:
no problem just figured it out.
thx

RGV

that one number is 5 times the size of the other

## 1. How do you define a natural number?

A natural number is a positive integer (whole number) that is greater than or equal to zero. It is often denoted by the symbol "N".

## 2. What does it mean for a natural number to not exist?

In mathematics, a natural number not existing means that there is no positive integer that satisfies a given condition or equation. In other words, there is no solution or value that can be assigned to the natural number in question.

## 3. Can you provide an example of a natural number that does not exist?

One example is the natural number that is both even and odd. Since these are mutually exclusive properties, there is no natural number that can fulfill both conditions simultaneously, thus it does not exist.

## 4. How can you prove that a natural number does not exist?

One way to prove that a natural number does not exist is by using logical reasoning and mathematical principles. This can involve showing that a given equation or statement leads to a contradiction or violates a fundamental mathematical concept.

## 5. Are there any consequences or implications of a natural number not existing?

Yes, if a natural number does not exist, it can have significant implications in various mathematical and scientific fields. For example, it can affect the validity of certain equations or theories, and may require further investigation and refinement of existing concepts.

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