Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

RolyPoly Group Title

"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?

  • 6 months ago
  • 6 months ago

  • This Question is Closed
  1. kc_kennylau Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Because it makes that \(\forall A,B\in\mathbb N, \frac AB\in\mathbb N\). @ikram002p am I right?

    • 6 months ago
  2. RolyPoly Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    We can also have A = 1, B = 3, but 1/3 \(\notin \mathbb N\)?

    • 6 months ago
  3. kc_kennylau Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    then i'm not right lol

    • 6 months ago
  4. kc_kennylau Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    oh, i see why 0's not natural, coz you can't have 0 things.

    • 6 months ago
  5. kc_kennylau Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    NATURal numbers are numbers that occur in the NATURE.

    • 6 months ago
  6. RolyPoly Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    -_- You can have nothing, right?

    • 6 months ago
  7. RolyPoly Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    There's something you CAN'T find in the nature though!

    • 6 months ago
  8. kc_kennylau Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    How do you count?

    • 6 months ago
  9. RolyPoly Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    From 0

    • 6 months ago
  10. kc_kennylau Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    cool

    • 6 months ago
  11. kc_kennylau Group Title
    Best Response
    You've already chosen the best response.
    Medals 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 non-negative 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

    • 6 months ago
  12. Spacelimbus Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Not 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 \(\mathbb{N}_0\)

    • 6 months ago
  13. ikram002p Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    cuz 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)

    • 6 months ago
  14. RolyPoly Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    The 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.

    • 6 months ago
  15. kc_kennylau Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    The problem is that the question itself is already wrong. It isn't universal to exclude 0 from the list of natural numbers.

    • 6 months ago
  16. RolyPoly Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    But it also isn't universal to include 0 as well?

    • 6 months ago
  17. RolyPoly Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Warning: 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?

    • 6 months ago
    • Attachments:

See more questions >>>

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
  • 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.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.