That depends on whom you ask. The idea of what is "natural" evolves over time. I would answer yes, others here would answer no.
The science of Mathematics has many different branches, developed over thousands of years. There is disagreement in some of those branches as to the definition of natural numbers, specifically whether or not to include zero. Some authors begin the natural numbers with 0, corresponding to the non-negative integers 0, 1, 2, 3, …, whereas others start with 1, corresponding to the positive integers 1, 2, 3, …. Texts that exclude zero from the natural numbers sometimes refer to the natural numbers together with zero as the whole numbers, but in other writings, that term is used instead for the integers (including negative integers).
For the sake of clarity, I use "counting numbers" to indicate the set of non-negative integers that doesn't include zero and avoid the term "natural numbers" altogether, but that won't help you on a test. Answer whatever your teacher says, but if you were marked wrong for answering "yes" you could inquire about the Peano axioms or the von Neumann ordinal construction although we won't be held responsible for the result of that conversation if your teacher hasn't heard of them.
Yes
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they are almost all equivalent - whole numbers also have the number 0, which natural numbers (counting numbers) do not.
False
Well, honey, the intersection of the set of whole numbers and the set of natural numbers is the set of all positive integers. In other words, it's the numbers that are both whole and natural, which means it starts from 1 and goes on forever. So, there you have it, the sassy math lesson of the day!
Natural numbers consist of the set of all whole numbers greater than zero.
Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction. All natural and whole numbers are rational.