Despite my attempts, I have been trying to convince a certain person that Zero isn't really a number, just like -5 isn't a number...You can't count -23 bottles on the wall...
Even though the dictionary says,
1 a : the arithmetical symbol 0 or <null> denoting the absence of all magnitude or quantity
This person insists on saying that 0 is a number...Maybe I am wrong, maybe you can count zero, but more than likely, I just don't know how to explain it clearly....
Is Zero A Number..?
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AYHJA
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AYHJA
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For example...
If...Zero were a number...Why isn't it on the calendar..? Why not August 0, 2006..? Why isn't 00 a number....
The reason is because 0 is the Ace in a deck of cards, you can put it before the two, or after the king...It can be either or, one or the other...It is a point on a finite line that seperates one side, from the other side...
Just like Habib said it could be 0 degrees where he is things are freezing...Here, things freeze at 32 degrees...Now, if zero were a number, these two things would be equal, would they not..?
0 marks a point...It isn't a number like 7 or 22...Its a number in a sense, and has the value of having no value...It is a symbol, mor so than a number...Can I get a witness..?
If...Zero were a number...Why isn't it on the calendar..? Why not August 0, 2006..? Why isn't 00 a number....
The reason is because 0 is the Ace in a deck of cards, you can put it before the two, or after the king...It can be either or, one or the other...It is a point on a finite line that seperates one side, from the other side...
Just like Habib said it could be 0 degrees where he is things are freezing...Here, things freeze at 32 degrees...Now, if zero were a number, these two things would be equal, would they not..?
0 marks a point...It isn't a number like 7 or 22...Its a number in a sense, and has the value of having no value...It is a symbol, mor so than a number...Can I get a witness..?
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RIMFIRE
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Zero is just that†™‚¢‚¢¢¢¬…¡‚¬¢‚¬Å¡‚¦†
™‚¢‚¢¢¢¬…¡‚¬¢‚¬Å¡‚¦†™‚
¢‚¢¢¢¬…¡‚¬?0†™‚¢‚¢¢¢¬…¡‚¬?†™‚¢‚¢¢¢¬…¡‚¬¢‚¬Å¡‚¦..nothing.
It has no value, can†™‚¢‚¢¢¢¬…¡‚¬‚¢¢¢¬…¾
‚¢t be added to anything and it can†™‚¢‚¢¢¢¬…¡‚¬‚¢¢¢¬…¾
‚¢t be taken away from anything.
So no†™‚¢‚¢¢¢¬…¡‚¬¢‚¬Å¡‚¦.Zero, is not a number, it's a base point.
...and as the song goes:
"One is the loneliest number that you'll ever do"
Damn I'm good! :cheers:
™‚¢‚¢¢¢¬…¡‚¬¢‚¬Å¡‚¦†™‚
¢‚¢¢¢¬…¡‚¬?0†™‚¢‚¢¢¢¬…¡‚¬?†™‚¢‚¢¢¢¬…¡‚¬¢‚¬Å¡‚¦..nothing.
It has no value, can†™‚¢‚¢¢¢¬…¡‚¬‚¢¢¢¬…¾
‚¢t be added to anything and it can†™‚¢‚¢¢¢¬…¡‚¬‚¢¢¢¬…¾
‚¢t be taken away from anything.
So no†™‚¢‚¢¢¢¬…¡‚¬¢‚¬Å¡‚¦.Zero, is not a number, it's a base point.
...and as the song goes:
"One is the loneliest number that you'll ever do"
Damn I'm good! :cheers:
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raum
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:farao:
zero is a NUMERAL acceptable to numerical positional expression WITHIN NUMBERS, but is not in of itself a NUMBER.
Thus 10 is a number of two numerical positionings, while 0 is not a number.
The ultimate test is where it can be acted upon with mathematical operators.
The test"
1. addition. 1+0 = 1
2. subtraction 1-0 = 1, 0-1 = -1
3. multiplication 1*0 = 0
but,..
0/1 = INDIVISIBLE.
thus, 0 is not a number, in of itself.
Pharoah has spoken,.. the sun has risen.
zero is a NUMERAL acceptable to numerical positional expression WITHIN NUMBERS, but is not in of itself a NUMBER.
Thus 10 is a number of two numerical positionings, while 0 is not a number.
The ultimate test is where it can be acted upon with mathematical operators.
The test"
1. addition. 1+0 = 1
2. subtraction 1-0 = 1, 0-1 = -1
3. multiplication 1*0 = 0
but,..
0/1 = INDIVISIBLE.
thus, 0 is not a number, in of itself.
Pharoah has spoken,.. the sun has risen.
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trashtalkr
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I think it is a number though. There are different kinds of numbers. It is not a real number (1,2,3...) but it is an integer (0,1,2...). Integers are numbers also.
"If there were no eternal consciousness in a man, if at the bottom of everything there were only a wild ferment, a power that twisting in dark passions produced everything great or inconsequential; if an unfathomable insatiable emptiness lay hid beneath everything, what would life be but despair?"
Soren Kierkegaard
Soren Kierkegaard
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AYHJA
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Rim is always right..!
But tt...How can you still "think" its a number..? That's what I don't get...
Even if you are talking about sets, cardinal, natural, etc, the fact remains that 0 has no value...It is understood, sure, nobody is arguing that...But raum, as usual, summed it up beautifully...What's left to contradict that...
By all accounts, an integer is a natural number...And a natural number is the number 1 or any number obtained by adding one to it a number of times...
I think it is confused with being a character, but it isn't a number...I'll be waiting to read some academic proof of the otherwise...
Even if you are talking about sets, cardinal, natural, etc, the fact remains that 0 has no value...It is understood, sure, nobody is arguing that...But raum, as usual, summed it up beautifully...What's left to contradict that...
By all accounts, an integer is a natural number...And a natural number is the number 1 or any number obtained by adding one to it a number of times...
I think it is confused with being a character, but it isn't a number...I'll be waiting to read some academic proof of the otherwise...
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RIMFIRE
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QUOTE...But raum, as usual, summed it up beautifully...
WTF!
I get no respect......none I say!!
WTF!
I get no respect......none I say!!
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AYHJA
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I was posting the same thing in two windows, you must didn't see the updated version of the post..!
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Skinny Bastard
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Two ways to answer this one, the simple answer and the complicated mathematical answer.
The simple answer: Yes, of course zero is a number. (What, did you think it's maybe an animal or vegetable??? LMAO)
The mathematical answer: IT DEPENDS! What do you mean by "number." Seriously, I don't mean this as sarcasm. There are different sets of numbers that build up to the Real Number system (the unique complete ordered field).
Zero is clearly an element of the set of Real Numbers and is labeled the "additive identity" (the number that, when added to any other number x, doesn't change the value of x...I might note here that 1 is similarly the multiplicative identity or the number that, when multiplied by any other number x, doesn't change the value of x so using the 5+0=5 so it's not a number argument doesn't fly with me since 5*1=5). Thus, zero is a number, just as any other element of the set of Real Numbers is a number.
However, before you get to the Real Numbers, you probably start with the Counting Numbers or Natural Numbers, the set N = {1, 2, 3, ...} in set notation. Zero isn't a member of the set of Natural Numbers since you normally don't start counting with zero (addressing your calendar argument). A primitive society developing a counting system wouldn't think of "none" ... they'd start counting with "one." So, if by "number" you mean "the set of all Natural Numbers," then zero isn't among them. So, as I said...IT DEPENDS ON WHAT YOU MEAN BY "NUMBER".... You've got to learn to be more specific, man!
Of course, the concept of zero makes its appearance pretty early historically (the idea of using zero as a placeholder digit comes later, but that's notational, and a different story).
Let's ignore history and get back to mathematical development. After you have developed the Counting Numbers, you get the Positive Integers, and that's when zero steps onto the stage. The Positive Integers (more technically correct, the Non-Negative Integers) are the set of Natural Numbers and zero, usually designated P = {0, 1, 2, 3...} At that stage in the development of your number system, zero becomes a number.
The next step is usually the set of all Integers, which is the set of Natural Numbers, zero, and the additive inverses of the Natural Numbers (negative numbers). Thus, I = {..., -3, -2, -1, 0, 1, 2, 3,...}
We could stop here..... but why?
To get to the real numbers, we need to add multiplicative inverses for all numbers except zero, thus, through the group operations of addition and multiplication, building Q, the set of all Rational Numbers, which is an "ordered field" in group theory terminology. It's ordered because you can always compare two distinct numbers and one of them will be larger than the other. It's a field because it follows the field axioms for addition + and multiplication X (and every element has an inverse under these operations, except there's no inverse for zero under multiplication). And then finally, we add the irrational numbers to get the property of completeness (viz., every set which is bounded above has a least upper bound), and voila! the Real Numbers, the unique complete ordered field. All these different stages of development of the Real Number system contain zero, except for the first stage, the Natural Numbers.
If you limit your definition of "number" to the Natural Numbers, then, no, zero isn't a "number." Of course, under that definition, 1/2 and -5 and pi aren't "numbers" either. And who wants to leave out pi? Where would we be at Thanksgiving without pi?
So zero gets my vote as a number, unless you are defining "number" in the restricted mathematical sense of Counting Numbers only.
The simple answer: Yes, of course zero is a number. (What, did you think it's maybe an animal or vegetable??? LMAO)
The mathematical answer: IT DEPENDS! What do you mean by "number." Seriously, I don't mean this as sarcasm. There are different sets of numbers that build up to the Real Number system (the unique complete ordered field).
Zero is clearly an element of the set of Real Numbers and is labeled the "additive identity" (the number that, when added to any other number x, doesn't change the value of x...I might note here that 1 is similarly the multiplicative identity or the number that, when multiplied by any other number x, doesn't change the value of x so using the 5+0=5 so it's not a number argument doesn't fly with me since 5*1=5). Thus, zero is a number, just as any other element of the set of Real Numbers is a number.
However, before you get to the Real Numbers, you probably start with the Counting Numbers or Natural Numbers, the set N = {1, 2, 3, ...} in set notation. Zero isn't a member of the set of Natural Numbers since you normally don't start counting with zero (addressing your calendar argument). A primitive society developing a counting system wouldn't think of "none" ... they'd start counting with "one." So, if by "number" you mean "the set of all Natural Numbers," then zero isn't among them. So, as I said...IT DEPENDS ON WHAT YOU MEAN BY "NUMBER".... You've got to learn to be more specific, man!
Of course, the concept of zero makes its appearance pretty early historically (the idea of using zero as a placeholder digit comes later, but that's notational, and a different story).
Let's ignore history and get back to mathematical development. After you have developed the Counting Numbers, you get the Positive Integers, and that's when zero steps onto the stage. The Positive Integers (more technically correct, the Non-Negative Integers) are the set of Natural Numbers and zero, usually designated P = {0, 1, 2, 3...} At that stage in the development of your number system, zero becomes a number.
The next step is usually the set of all Integers, which is the set of Natural Numbers, zero, and the additive inverses of the Natural Numbers (negative numbers). Thus, I = {..., -3, -2, -1, 0, 1, 2, 3,...}
We could stop here..... but why?
To get to the real numbers, we need to add multiplicative inverses for all numbers except zero, thus, through the group operations of addition and multiplication, building Q, the set of all Rational Numbers, which is an "ordered field" in group theory terminology. It's ordered because you can always compare two distinct numbers and one of them will be larger than the other. It's a field because it follows the field axioms for addition + and multiplication X (and every element has an inverse under these operations, except there's no inverse for zero under multiplication). And then finally, we add the irrational numbers to get the property of completeness (viz., every set which is bounded above has a least upper bound), and voila! the Real Numbers, the unique complete ordered field. All these different stages of development of the Real Number system contain zero, except for the first stage, the Natural Numbers.
If you limit your definition of "number" to the Natural Numbers, then, no, zero isn't a "number." Of course, under that definition, 1/2 and -5 and pi aren't "numbers" either. And who wants to leave out pi? Where would we be at Thanksgiving without pi?
So zero gets my vote as a number, unless you are defining "number" in the restricted mathematical sense of Counting Numbers only.
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Skinny Bastard
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additional information on why zero IS a number can be found HERE(including a discussion of when zero is a symbol or placeholder and not a number).
I also liked this explanation from Wikipedia;
0 as a number
0 is the integer that precedes the positive 1, and follows −1. In most (if not all) numerical systems, 0 was identified before the idea of 'negative integers' was accepted.
Zero is an integer which quantifies a count or an amount of null size; that is, if the number of your brothers is zero, that means the same thing as having no brothers, and if something has a weight of zero, it has no weight. If the difference between the number of pieces in two piles is zero, it means the two piles have an equal number of pieces. Before counting starts, the result can be assumed to be zero; that is the number of items counted before you count the first item and counting the first item brings the result to one. And if there are no items to be counted, zero remains the final result.
While mathematicians all accept zero as a number, some non-mathematicians would say that zero is not a number, arguing one cannot have zero of something. Others hold that if you have a bank balance of zero, you have a specific quantity of money in your account, namely none. It is that latter view which is accepted by mathematicians and most others.
Almost all historians omit the year zero from the proleptic Gregorian and Julian calendars, but astronomers include it in these same calendars. However, the phrase Year Zero may be used to describe any event considered so significant that it virtually starts a new time reckoning.
I also liked this explanation from Wikipedia;
0 as a number
0 is the integer that precedes the positive 1, and follows −1. In most (if not all) numerical systems, 0 was identified before the idea of 'negative integers' was accepted.
Zero is an integer which quantifies a count or an amount of null size; that is, if the number of your brothers is zero, that means the same thing as having no brothers, and if something has a weight of zero, it has no weight. If the difference between the number of pieces in two piles is zero, it means the two piles have an equal number of pieces. Before counting starts, the result can be assumed to be zero; that is the number of items counted before you count the first item and counting the first item brings the result to one. And if there are no items to be counted, zero remains the final result.
While mathematicians all accept zero as a number, some non-mathematicians would say that zero is not a number, arguing one cannot have zero of something. Others hold that if you have a bank balance of zero, you have a specific quantity of money in your account, namely none. It is that latter view which is accepted by mathematicians and most others.
Almost all historians omit the year zero from the proleptic Gregorian and Julian calendars, but astronomers include it in these same calendars. However, the phrase Year Zero may be used to describe any event considered so significant that it virtually starts a new time reckoning.
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