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Question

Give arguments in support of the statement that there does not exist the largest natural number.

Solution
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Assume the existence of a largest natural number $$p$$

Being the largest natural number, $$p$$ cannot be followed by a greater natural number.
i.e., $$p + 1 ≤ p$$
Now subtracting $$p$$ from both sides,
$$\Rightarrow 1 ≤ 0$$ , which is not true.

This shows that the assumption of $$p$$ leads to a contradiction.
Hence, there does not exist any largest natural number.

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