Is Zero Discrete? - Math Explained

In summary: Discrete was the answer I received. And thanks the poster for the immediate answer.In summary, natural numbers are considered discrete since they are a countable set, and zero is a member of the natural numbers, making it also discrete. However, it may not make sense to talk about a single number, such as zero, as being discrete.
  • #1
Atlas3
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Is zero discrete?
 
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  • #3
I would think that any single object is "discrete", but perhaps I am using a different definition of "discrete".
What definition are you using?
 
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  • #4
jedishrfu said:
Natural numbers are known as discrete numbers since they are a countable set. Zero is a member of the natural numbers, hence zero is discrete.

http://en.wikipedia.org/wiki/Natural_number
Zero is a real number too!
Anyway, I think the question is meaningless. Discreteness isn't a property of a single number!
 
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  • #5
I have a simple counting question and the use of decimals. Possibly I want to count decimal fractions differently for the purposes of defining the range of something. A different number line of a kind? Folded eventually. Does this seem like a practical forum to ask this type of question?
 
  • #7
HallsofIvy said:
What definition are you using?
Quantized. I'll open a new thread from here on
 
  • #8
Shyan said:
Zero is a real number too!
Anyway, I think the question is meaningless. Discreteness isn't a property of a single number!
It is a quantity. Correct me if its not that please.
 
  • #9
Atlas3 said:
It is a quantity. Correct me if its not that please.
What is a quantity? If you mean discreteness, then no, its a concept!
 
  • #10
Shyan said:
What is a quantity? If you mean discreteness, then no, its a concept!
I mean I can have zero of something
 
  • #11
You started by asking 'Is 0 discrete'. I asked what definition of 'discrete' you are using and you responded "quantized". That is a term used in Quantum Physics and is meaningless here. Now you are asking whether '0' is a quantity. Yes, if you ask a store owner, "how many boxes of cigars do you have", the store owner could well answer, 'none'. '0' is definitely a 'quantity'.
 
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  • #12
HallsofIvy said:
You started by asking 'Is 0 discrete'. I asked what definition of 'discrete' you are using and you responded "quantized". That is a term used in Quantum Physics and is meaningless here. Now you are asking whether '0' is a quantity. Yes, if you ask a store owner, "how many boxes of cigars do you have", the store owner could well answer, 'none'. '0' is definitely a 'quantity'.
Like X.
 
  • #14
micromass said:
What is X?
I mean like a algebra teacher refers to the quantity X.
 
  • #15
You mean the variable X?
 
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  • #16
micromass said:
You mean the variable X?
Yes but not variable Zero
 
  • #17
Atlas3 said:
Yes but not variable Zero
Zero is not a variable -- it is a constant, just like 1 or 5 or -213.7 or ##\pi##. A variable can represent an arbitrary number*. Zero is a very specific number.

* - My context here is elementary algebra of the real number line, so I'm not considering variables outside that realm.
 
  • #18
i didn't state varied zero. Constant zero. I wasn't being funny
 
  • #19
Atlas3 said:
i didn't state varied zero. Constant zero. I wasn't being funny
You said "variable Zero" in post #16, which I quote again, below. How else was I to interpret "variable Zero"?
Atlas3 said:
Yes but not variable Zero
 
  • #20
Perhaps you could tell us what are studying and how you came to asking about zero being discrete.
 
  • #21
Every time you are asked to clarify something, you answer with another ambiguity. I am starting to think that this whole thread was just a joke. Your original question was "Is 0 discrete?" I asked what you meant by "discrete" and your response was "like X". Please tell us what you think the word "discrete" means!
 
  • #22
Mark44 said:
You said "variable Zero" in post #16, which I quote again, below. How else was I to interpret "variable Zero"?
It has the word not preceding that word
 
  • #23
jedishrfu said:
Perhaps you could tell us what are studying and how you came to asking about zero being discrete.
I'll try. If I can figure out the forum post editor for markup when I get the time on a computer right now it is cumbersome on iphone
 
  • #24
Mark44 said:
You said "variable Zero" in post #16, which I quote again, below. How else was I to interpret "variable Zero"?
Atlas3 said:
It has the word not preceding that word
Whatever.
What you said was extremely unclear. I have no idea what you're trying to say with "not variable Zero".

Back to the original question, "Is zero discrete?" A set of numbers that is separated is discrete, such as {0, 1, 2, ...,n, n + 1, ...} or {1/4, 1/2, 3/4, 1, 5/4, ...}. I'm not sure it makes any sense to talk about a single number as being discrete.
 
  • #25
HallsofIvy said:
Every time you are asked to clarify something, you answer with another ambiguity. I am starting to think that this whole thread was just a joke. Your original question was "Is 0 discrete?" I asked what you meant by "discrete" and your response was "like X". Please tell us what you think the word "discrete" means!
I was asking if zero is considered a discrete value meaning nil but countable. Wasn't asking a philosophical question or making a joke. Just asking if in numbers it is considered the same as any other. Discrete was the answer I received. And thanks the poster for the immediate answer.
 
  • #26
Mark44 said:
Whatever.
What you said was extremely unclear. I have no idea what you're trying to say with "not variable Zero".
Not a variable value. Invariant
 
  • #27
Mark44 said:
Whatever.
What you said was extremely unclear. I have no idea what you're trying to say with "not variable Zero".

Back to the original question, "Is zero discrete?" A set of numbers that is separated is discrete, such as {0, 1, 2, ...,n, n + 1, ...} or {1/4, 1/2, 3/4, 1, 5/4, ...}. I'm not sure it makes any sense to talk about a single number as being discrete.
I just answered you again above. You were quicker with another post and missed the clarification. It's above
 
  • #28
Question has been asked and
Atlas3 said:
I have a simple counting question and the use of decimals. Possibly I want to count decimal fractions differently for the purposes of defining the range of something. A different number line of a kind? Folded eventually. Does this seem like a practical forum to ask this type of question?
Please start a new thread for this question.
 
  • #29
Mark44 said:
Question has been asked and

Please start a new thread for this question.
Am I on a deadline. I'll ask in a new thread as suggested. I had work to do besides forum posting
 
  • #30
No, 0 is not discrete. In fact, 0 being discrete makes no mathematical sense. Unless you can give a precise definition of the term discrete that you are using.
 
  • #31
jedishrfu said:
Natural numbers are known as discrete numbers since they are a countable set. Zero is a member of the natural numbers, hence zero is discrete.

http://en.wikipedia.org/wiki/Natural_number

A countable set need not have the discrete topology.
 
  • #32
I think that this thread has run its course and suggest we close it.
 
  • #33
I agree. The OP's question has been asked and answered.
 

1. What is a discrete number?

A discrete number is a whole number that can be counted or measured in exact units, such as 1, 2, 3, etc. It is distinct and separate from other numbers.

2. Is zero considered a discrete number?

Yes, zero is considered a discrete number because it is a whole number that can be counted or measured in exact units. It is also distinct and separate from other numbers.

3. How is zero different from other discrete numbers?

Zero is different from other discrete numbers because it is the only number that represents nothing or the absence of quantity. It is also the only number that is neither positive nor negative.

4. Can zero be classified as both discrete and continuous?

No, zero cannot be classified as both discrete and continuous. It is only considered a discrete number because it is a whole number, and it cannot be divided into smaller units. It does not have the properties of a continuous number, which can be infinitely divided into smaller units.

5. How is zero used in mathematics?

Zero is used in mathematics as a placeholder to represent the absence of quantity, as well as to indicate the start of a number line. It is also used in operations such as addition, subtraction, and multiplication, and it has its own set of mathematical properties and rules.

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