Yes.
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Yes a real number is a natural since real is natural so anything real is natural and so a real number is natural.
An Archimedean property is the property of the set of real numbers, that for any real number there is always a natural number greater than it.
It is not a natural number but it is an integer and a real number.
Natural number are a special kind of real number. They both are large without bounds. For every real number there is a larger natural number and for every natural number there is a larger real number.
The prime number of 11 is a real and natural number