True or false depending on who you ask. It is a matter of convention. Long ago before people accepted the concept of 0, it wasn't included. Then when people began making formal constructions of the natural numbers in the 19th century they saw that it made a lot of sense (read: it was convenient) to include 0. People are still pretty well split on it today with allegiances sometimes depending on the exact field of the person in question.
If you were to ask me personally: yes yes yes yes yes. But there are people out there who would say no. It comes down to preference of convention. However, as noted already, when you actually try to axiomatically or set theoretically construct the natural numbers, it is almost downright foolish to not include 0 (though of course that is an opinion too, but most people who have studied such constructions would likely agree).
Mathematicians are not agreed on this point. Some use N and N+ to distinguish between the set of Natural numbers including 0, and not including 0.
The set of natural numbers plus zero is the set of all non-negative integers. Please note that the definition for the set of natural numbers is ambiguous. Some definitions include zero, while others exclude it.
Yes.
The extended set of natural numbers, or the non-negative integers.
Integers
Whole numbers are the set of natural or counting numbers inclding zero
Mathematicians are not agreed on this point. Some use N and N+ to distinguish between the set of Natural numbers including 0, and not including 0.
The set of natural numbers plus zero is the set of all non-negative integers. Please note that the definition for the set of natural numbers is ambiguous. Some definitions include zero, while others exclude it.
False.
Yes.
0,1,2,3...
Zero (0) is in the set of whole number. The only difference between the set of whole numbers and counting numbers is that the whole numbers contain zero. {0,1,2,3...}
The set of integers, Z.
True. Zero is in the set of whole numbers, integers, rational numbers and real numbers but not natural numbers. Natural numbers are often referred to as the "counting numbers" or how you learned to count. When we are teaching little children numbers, we never start with zero or negative numbers - just 1, 2, 3...
False. The collection of natural numbers is an example of a set, not an element. An element is an individual member of a set, while the collection of natural numbers is a set itself.
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!
The extended set of natural numbers, or the non-negative integers.