Is zero a cardinal number?

Discussion in 'Number Theory' started by in2infinity, Apr 20, 2022.

  1. in2infinity

    in2infinity

    Joined:
    Apr 20, 2022
    Messages:
    6
    Likes Received:
    0
    Hi there. I was having a real problem finding out is zero was a cardinal number or not?
    This website says it is...

    https://www.yourdictionary.com/cardinal-number

    and this website says it is not?

    https://byjus.com/maths/cardinal-numbers/

    In fact the issue seems to be very unclear.

    Zero is not in the ordinal set as there is no ZEROth step. Is that right?

    I want to know is I am standing at zero, and a Take a step, Do I count the zero number, and is this a cardinal number?

    I apologise if this seems like a very simple maths question. Thanks in advance for your help..
     
    in2infinity, Apr 20, 2022
    #1
  2. in2infinity

    MathLover1

    Joined:
    Jun 27, 2021
    Messages:
    2,989
    Likes Received:
    2,884
    The cardinal number of the empty set is is 0.
     
    MathLover1, Apr 24, 2022
    #2
  3. in2infinity

    ddinunno

    Joined:
    Mar 1, 2023
    Messages:
    15
    Likes Received:
    2
    Location:
    28037
    This is a frequent challenge in software program. It is said that, "programmers are often off by 1." - just for the type of issue you indicated. Where do I start?

    Is "next Sunday" the one coming up or the one after that?

    Is Maryland 1 state away from Virginia or - since they touch - is it 0 distance. Historically, some cultures would count Maryland as 1 and Virginia as 2. So, Virginia is two states away. (Of course, historically, Maryland and Virginia did not exist.) Also, historically zero did not exist.

    I agree that while 0 is not a counting number it is the cardinality of the null set.

    P.S. Historically 1 was considered a prime number. (How more prime can you get than 1?)
     
    ddinunno, Mar 31, 2023
    #3
  4. in2infinity

    conway

    Joined:
    Nov 28, 2023
    Messages:
    155
    Likes Received:
    4
    I find this thread fascinating. The real issue is in how we define zero, and its cardinality. An empty "set" is the absence of a numerical quantity.

    It is NOT, absent a dimensional unit quantity. It is this quantity that we should philosophically count, when we are standing on zero, and moving to 1 or negative 1.

    Consider (1 + -1 = 0).

    This is proof of the space of zero. Or the dimensional unit quantity.

    This is also relative to how we define zero. It is currently defined as a "whole number". Yet numbers are defined as numerical quantities. Yet zero is the absence of a numerical quantity. Therefore logically it should not even be defined as a number.

    Give zero a dimensional unit quantity. Along with all other numbers. Allow it to remain without a numerical quantity. And you can answer the above questions. As well as solve for division by zero.
     
    conway, Sep 23, 2024
    #4
Ask a Question

Want to reply to this thread or ask your own question?

You'll need to choose a username for the site, which only take a couple of moments (here). After that, you can post your question and our members will help you out.
Similar Threads
There are no similar threads yet.
Loading...