Sure there are greater numbers. For example, 4 is greater than 3.
If you mean "... no greatest number", the reason is that you can always add one more, and get a number that is even greater. Thus, for example, 10 is not the greatest number, because you can add one and get 11. 11 is not the greatest number either, because you can add one and get 12. Etc.
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A natural counting number is a positive number greater than 0
it is called a counting number or a natural number
No because natural numbers are whole numbers greater than 0
5 is a natural number, as it is an integer greater than zero. It is a whole number, an integer, and a rational number.
How about 8 as one example