example are 1,2,3,4,5,6,7,8,9,10
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No. Not in hexadecimal, but yes if you are counting in base 21, for example.
A counting number is the numbers you lear as a little kid, counting numbers are one and up. Integers include the counting numbers, 0, and the opposite (negative) of counting numbers. So yes, a counting number or the opposite of a counting number is an integer.
Natural numbers are the counting numbers: 1, 2, 3, 4, 5, etc... Integers are positive and negative counting numbers, and zero. So, an integer that is not a counting number could be 0 or any negative integer.
No. 3.6427 is real and rational, but not a counting number.
1 is the counting number that is neither a prime number nor a composite number.