A community for students. Sign up today!
Here's the question you clicked on:
 0 viewing
 one year ago
"The numbers 1, 1+1=2, 2+1=3, etc. are said to be natural; it is assumed that none of these numbers is zero".
Why do we have/need such an assumption?
 one year ago
"The numbers 1, 1+1=2, 2+1=3, etc. are said to be natural; it is assumed that none of these numbers is zero". Why do we have/need such an assumption?

This Question is Closed

kc_kennylau
 one year ago
Best ResponseYou've already chosen the best response.1Because it makes that \(\forall A,B\in\mathbb N, \frac AB\in\mathbb N\). @ikram002p am I right?

RolyPoly
 one year ago
Best ResponseYou've already chosen the best response.1We can also have A = 1, B = 3, but 1/3 \(\notin \mathbb N\)?

kc_kennylau
 one year ago
Best ResponseYou've already chosen the best response.1then i'm not right lol

kc_kennylau
 one year ago
Best ResponseYou've already chosen the best response.1oh, i see why 0's not natural, coz you can't have 0 things.

kc_kennylau
 one year ago
Best ResponseYou've already chosen the best response.1NATURal numbers are numbers that occur in the NATURE.

RolyPoly
 one year ago
Best ResponseYou've already chosen the best response.1_ You can have nothing, right?

RolyPoly
 one year ago
Best ResponseYou've already chosen the best response.1There's something you CAN'T find in the nature though!

kc_kennylau
 one year ago
Best ResponseYou've already chosen the best response.1"There is no universal agreement about whether to include zero in the set of natural numbers: some define the natural numbers to be the positive integers {1, 2, 3, ...}, while for others the term designates the nonnegative integers {0, 1, 2, 3, ...}. The former definition is the traditional one, with the latter definition having first appeared in the 19th century." https://en.wikipedia.org/wiki/Natural_number

Spacelimbus
 one year ago
Best ResponseYou've already chosen the best response.0Not sure if I understand the concept of this question. But I remember the following words from my Professor "First thing, you always do when you buy a boot about Mathematics, check on their definition of \(\mathbb{N}\)" What he meant by that, was that whether or not \(0 \in \mathbb{N}\) or not is still a big discussion. For references check for example Zorich Analysis 1, Blatter Analysis and so on. Also consider the notation \(\mathbb{N}_0\)

ikram002p
 one year ago
Best ResponseYou've already chosen the best response.0cuz 0 is the identity of any groupe on the binary operation of addition , so it must be UNIQE its thm from (elementary properties of groups)

RolyPoly
 one year ago
Best ResponseYou've already chosen the best response.1The footnote of this quotation was as follows: "Given two elements N and E, say, we can construct a field by the rules N+N=N, N+E=E, E+E=N, N\(\cdot\)N=N, N\(\cdot\)E=N, E\(\cdot\)E=E. Then, in keeping with our notation, we should write N=0, E=1 and hence 2=1+1=0. To exclude such number systems, we require that all natural field elements be nonzero" Basically, I don't know what's going on here.

kc_kennylau
 one year ago
Best ResponseYou've already chosen the best response.1The problem is that the question itself is already wrong. It isn't universal to exclude 0 from the list of natural numbers.

RolyPoly
 one year ago
Best ResponseYou've already chosen the best response.1But it also isn't universal to include 0 as well?

RolyPoly
 one year ago
Best ResponseYou've already chosen the best response.1Warning: Please ignore the following.  Should 0 be included in the set of natural numbers?  <Saying I> No, \(0\notin \mathbb N\) The numbers 1, 1+1=2, 2+1=3, ... are said to be natural. Given two elements N and E, we can struct a field by the rules (i) N+N=N (ii) N+E=E (iii) E+E=N (iv) N\(\cdot\)N = N (v) N\(\cdot\)E = N (vi) E\(\cdot\)E = E Then in keeping with our notation, we should be N=0, E=1. From (iii), E+E = N, so, we have 1+1 = 0 However from the first statement, we have 1+1=2 \(\ne\) 0, so we need to exclude 0. Problems: 1) Why would we construct such a field with rules (i) to (vi), particularly with rule (iii)? 2) What would happen if we picked some other values for N and E?
Ask your own question
Ask a QuestionFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.