The Number 1 and the Prime Numbers.

The original definition was: “A prime number is a natural number that is divisible exclusively by itself and 1”.

But now the definition is: “A prime number is a natural number that is greater than 1 and divisible exclusively by itself and 1”.

That is cheating!

Perhaps O:)

No rush :wink:

So what do you think that means or is inferring to?

Isn’t that the prevailing morality? - “Thy rules are thus - but not for us.”

If I may answer:

It more or less reflects what we have to deal with more and more in modern times: the rulers enforce everything in the way that suits them best, and this is often to the detriment of all other people. The sciences are becoming more and more dependent, the culture as a whole is becoming more and more victimized.

Agreed.

Absolutely.

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Indeed, historically many mathematicians up to the nineteenth century thought of 1 as prime – Henri Lebesgue (1875–1941) is usually said to have been the last professional mathematician to call 1 prime. (The Greeks didn’t regard 1 as prime, but that’s because they didn’t regard it as a number at all!)

[size=85]http://www.foster77.co.uk/Foster,%20Mathematics%20in%20School,%20Why%20isn’t%201%20a%20prime%20number.pdf[/size]
Why isn’t 1 a prime number? - Colin Foster
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[size=85]https://blogs.scientificamerican.com/roots-of-unity/why-isnt-1-a-prime-number/[/size]
Why Isn’t 1 a Prime Number? - Scientific American Blog Network
2 Apr 2019 — For that reason, 1 couldn’t have been prime — it wasn’t even a number. Ninth-century Arab mathematician al-Kindī wrote that it was not a number and therefore not even or odd. The view that 1 was the building block for all numbers but not a number itself lasted for centuries.
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2 is prime. Rebuttal: Because even numbers are composite, 2 is not a prime.


  • 1 wasn’t considered a number by the Greeks and Arabs? Who knew…
  • Why can’t 2 be both prime and composite?

Does the OECD Math Department know about this? I wonder what their take is on such numerical anomalies?
As philosophers, I say we have free-rein on such matters, and declare them as how we see fit.

…and so …I’m relabelling 1, and declaring 2 of dual numerical status. :handgestures-thumbsup:

What I am curious about is why 1 wasn’t considered a “number”. That just seems bizarre. :-k

“Four people voted - list the number of votes” -
[list]* 3 votes in favor
[] none against.
[/
:m][/list:u]
:confused:

Maybe it was one of those “perfect fraud-free election” things. O:)

Yes, the number 2 is also a problem. Either we allow the number 1 to be a prime number again, or we also take the number 2 out of the prime number set and say: “Within the whole positive number set, the number 2 can only be divided by itself and by 1, because there is only one positiv number which is smaller than 2”. So then the new definition would be: “A prime number is that integer positive number which is greater than 2 and divisible only by itself and 1”. In this case, the prime numbers would begin with the number 3.

This would lead to other problems. So we should leave it at the first definition, so that 1 and 2 are prime numbers: “A prime number is that integer positive number which is divisible by itself and 1”.

1 was considered a unit, and a number was composed of multiple units, is why.

Lol

Should the number 1 still not be allowed to be a prime number?
You may select 1 option

Yes. 3 43%

No. 4. 57%

I do not care at all. 0. No votes

Total votes : 7

I guess the Mathematician should know what numbers are applicable to use in what calculations and circumstance, regardless of category.

Mathematicians are the ones among scientists who are the least corrupt (well, some people say that mathematics is not a science at all), but scientists want money, and that is why they have been bought more and more.

That had to come from a society far too over-encumbered by semantics. :neutral_face:

The worship of the number 1 can culturally work like a taboo. Ancient Greeks believed that everything is uniform, abyssal, delimited (everything also in the aesthetic sense). The number 1 means “unit”.

Since the conquests of Alexander the Great, the special role of the 1 declined in Ancient Greece.

I don’t see the connection. :-k

Isn’t it more likely that it is the word “unit” that means 1?

Yes, it is also the case that children first learn the word “one” and then the number “1”. But in the beginning, they can’t separate the two. For children, “one” and “1” initially mean the same. It is only later that they come to understand the difference. And that’s probably how it was with the Ancient Greeks too - on a higher level of course - in their early times.

I guess I never got to that stage :blush:

  • Or maybe I am just an old Greek soul. :smiley:

So what - exactly - is that difference?

You could understand the meaning of the word “one” before you could understand the meaning of the number “1”.

Young children know very early what words are, but they separate the numbers - as numbers (and no longer as words) - from the words a bit later, when they begin to count with their fingers (counting, firstly accompanied by speaking, later no longer). When they have learned to count, they are fit for arithmetic and therefore for mathematics lessons - not before.


When a culture begins, it’s not much different, but the level is higher (after all, it’s mostly adults). The question is, whether and which words are holy or not, and later eventually, whether and which numbers are holy or not. It depends on the conditions of the early culture (which people and which environment?).

The best known of the Ancient Greek mathematicians who have come down to us and who were still mystical/religious about it, is Pythagoras. The time I have just spoken about is even far before Pythagoras.


Okay - I think i can see where you are going with this -

I see these things a little differently. I know that people think in different ways - I am referred to an an “analytical reductionist”.

An analytical reductionist is someone who reduces issues down to their basic concepts. We discern the “conceptual” or the “divine” - the abstract concept involved - the angels, demons, devils, and gods. And we tend to be able to easily understand the simple logic of what we each say as being exactly true or false or just too vague to be certain about. We tend to all agree very much on anything we have much education about. We learn from each other very quickly. And when I read about what people like Plato, Aristotle, and even Jesus have said - it all seems almost too obvious to mention.

Similar things happen with other kinds of minds - they see the “sense” all of the others of “like minds” are trying to explain. They see it instantly - whether it actually makes any real sense or not. That is why observers are chosen by their mind-type. - so they can relay what the intention really was to those concerned with whatever they said (dogs can’t see color) - much like a language interpreter but more like a thought interpreter.

So when you ask of the difference between the number 1 and word or concept of one - I have to scratch around to try to discern any difference. To me it turns out to be merely superficial semantics. And now that you have raised this issue of social beginnings I have to believe that with Plato, Hebrews, and the like - it was the same.

I doubt that their society started as one kind of mind that grew through time to become another kind. It seems much more likely to me that in the mix of minds they had when they started, a type of Darwinian interaction caused dominance of a variety of types of cultural norms and ideas. And through time, different aspects of those norms got more or less attention by others who could identify with them. Often they form identifiable groups.

And those groups, like the soap bubbles foaming up from the stream of life’s splashing issues, interact and role around each other rising, growing, and at times bursting while they form the world of mankind.

And in this vein of number vs concept and original prime vs new age - to us analytical reductionists - it is all just - “a rose by any other name” ( - but get your bloody words straight). :wink:

1x1=1

Get over it!

WHo gives a fuck anyway. What is the use of Prime Numbers such that this question is important?