"negative" prime numbers
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Dr.Peterson
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First, who told you there are no negative prime numbers? Second, what definition are you using?
The fact is, there are some contexts in which we can adjust the definition to allow for negative prime numbers. So you can't really say that we can't define primes in such a way. Definitions are tools of mathematics, and can be designed according to need.
The real question is (a) how whatever definition you are using implies that -5 is not prime, and (b) why whoever wrote that definition chose not to allow it within their context. That could be a good discussion, if you want to tell us more about the context of your question, and your own thinking.
If you searched for your question, you might come across this, which gives something like the answer I would give:
Can negative numbers be prime?
Can negative numbers be prime? Another page about Prime Numbers and related topics.
shahar
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From the text:
Numbers that divide one are called units. Two numbers a and b for which a is a unit times b are called associates. So the divisors a and -a of b above are associates.
I don't understand what is written in this paragraph - Can you explain to me by another word (and example... )
Numbers that divide one are called units. Two numbers a and b for which a is a unit times b are called associates. So the divisors a and -a of b above are associates.
I don't understand what is written in this paragraph - Can you explain to me by another word (and example... )
First, who told you there are no negative prime numbers? Second, what definition are you using?
The fact is, there are some contexts in which we can adjust the definition to allow for negative prime numbers. So you can't really say that we can't define primes in such a way. Definitions are tools of mathematics, and can be designed according to need.
The real question is (a) how whatever definition you are using implies that -5 is not prime, and (b) why whoever wrote that definition chose not to allow it within their context. That could be a good discussion, if you want to tell us more about the context of your question, and your own thinking.
If you searched for your question, you might come across this, which gives something like the answer I would give:
Can negative numbers be prime?
Can negative numbers be prime? Another page about Prime Numbers and related topics.primes.utm.edu
pka
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This is a pet peeve of mine. I once caught Keith Devlin in this error. Many have said that a prime is an integer having only itself and one as divisors.
But under that statement, [imath]\bf 1\text{ is prime}[/imath] which we definitely can't have. SEE HERE & Here2
So define a prime is an integer with exactly two divisors.
Using that definition are neither of [imath]-2\text{ or }4[/imath] a prime?
Dr.Peterson
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You mean, from the link I provided?
Let's not start there. Please answer my questions about your own context, rather than try to understand one that is new to you - and, in fact, to me. (I provided the link only to show that the answer can be varied, not intending to discuss the specifics, which you are not ready for. The specifics of my own version of the answer would be different.)
What definition are YOU using?
What did someone say to you that indicated that negative numbers can't be prime, without giving a reason?
We can only discuss this based on a specific definition. (pka has provided two possible ways to say the definition, one not quite accurate; we need to see yours.) There is a lot to discuss without touching the bit you are asking about.
shahar
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I use the definition of the Israeli Pyschometry that is SAT-like exam that people who want to attend university and high academic institute in Israel must pass.
The reason of the definition as I explore is that Fundamental theorem of arithmetic is needed to define it like that and that is the reason I think.
The reason of the definition as I explore is that Fundamental theorem of arithmetic is needed to define it like that and that is the reason I think.
Dr.Peterson
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I presume you are not quoting the definition because it is not in English; but please translate it, so we can be sure we are starting in the same place. Not quoting your definition feels like refusal to cooperate, and prevents discussion.
You are right that the Fundamental Theorem of Arithmetic lies behind the choice of which numbers are called prime. But I really need you to tell me your own thinking, so I can focus on the parts of the discussion that are relevant to you. Do you think there is a reason negative numbers should be allowed to be primes? Do you think that the definition you are given does apply to negative numbers? What is your specific concern?
To put it another way, what would you do or think differently depending on the answer?
The main reason negative numbers are not considered prime is simply that the concept of prime numbers came before the concept of negative numbers, and there is no reason to extend it. Most applications of the concept involve only the natural numbers; that is what number theory primarily deals with.
A second reason is that if we do extend the concept (by changing the definition), things get more complicated, which is perhaps the main point of the second answer in the link. In particular, the FTA would have to be stated differently.
shahar
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Look as I know mathematics invented by humans. So, if we say we are using it as a invention and not discovery we can say any thing. I ask it because the books that prepare you to the Pyschometry say that it need to be greater than one.
But in the Pyschometry there is a page of formula, and say thing like:
0 is not negative number and not positive number.
1 is not prime number.
In Page 2 in the link:
I just wonder why that it not mention in the formula page. People explain to me that only what it written is compulsive to use in the test. And NOW I see that there is implicit rule that not mention explicitly.
So that a bug in the test. So I ask about it here.
(That is main reason for the exploration and inquiry that I made.
But in the Pyschometry there is a page of formula, and say thing like:
0 is not negative number and not positive number.
1 is not prime number.
In Page 2 in the link:
I just wonder why that it not mention in the formula page. People explain to me that only what it written is compulsive to use in the test. And NOW I see that there is implicit rule that not mention explicitly.
So that a bug in the test. So I ask about it here.
(That is main reason for the exploration and inquiry that I made.
Dr.Peterson
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Because you chose not to provide a translation as I requested, I had to get a Google translation of the whole document, the results of which are not very easy to read, and search through it in order to find the definition:
Prime: A positive integer that is divisible by two numbers only: itself and 1.
That is apparently what you eventually saw:
So, apparently, your question was whether the definition you were given excludes negative numbers, and you answered your own question by finally looking at the definition.
Why did it take you so long to figure this out, and why have you not even now actually quoted the definition that I asked for in the first place?
It was not at all clear in your initial question that you were asking about the meaning of your definition:
The word "why" doesn't communicate what you apparently meant to ask. This does not read as a request to explain the definition you were given and show that it excludes negative numbers; I took it to mean that you knew negative numbers are not prime, and thought it should be otherwise.
In the future, when we ask for a definition, please give the definition. And because of the language issues, please say more than you think you need to say, rather than less. If you had said in the first place "People tell me that negative numbers are not prime, but the information I have been given doesn't seem to say that", we could have answered you much more quickly, and with less trouble.
shahar
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O.K. Thanks.