This question is posed to those primarily in Pre-Calculus / Secondary education, but if you have anything interesting relating to your area of mathematics that'd be awesome to hear. Note, I'm a mathematics teacher, and my Masters in Mathematics was a few years ago...
Since University I have always defined $ \mathbb{N} =\{ 0 ,1,2,3...\} $ but across curriculum I have taught they insist $ \mathbb{N} =\{1,2,3...\} $. I have a few questions (I know they are very mixed across expertise), but answers to any would be amazing):
- Is there a preference at research level on how you define it or this dependent on what it is you are doing with the natural numbers?
- Is there a preference to how you define during University teaching?
- Is there a benefit to how we define it during secondary education?
I can see benefits to discounting 0 for summations and sequences during secondary education. But also, I often see the set $ \mathbb{Z}^+ $ introduced, which at this level of study is treated the same as $ \mathbb{N} \setminus \{0\} $ at this level.
What are your explanations, advantages and disadvantages?
Sorry this question is a little vague.