Prime Number Question

"... and 1"

Simple. 1 isn't different enough from 1 to be interesting. Unless 2=1..... (cue Don Atkinson)

Thanks Omer, LTD

All seems abit arbitrary/semantic to me...oh well, off for another crack at the Riemann Hypothesis

Cheers,

Tim
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Os nid Campagnolo yw hi, dyw hi ddim yn werth ei marcho...

quote:

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Originally posted by Tim Danaher:

All seems abit arbitrary/semantic to me

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Nothing could be more arbitrary or semantic than mathematics. It is arbitrary because it exists only inside the heads of human beings and semantic because it derives meaning in the same way. Prime numbers are just a consensus among people practicing mathematics.

Good luck with the Riemann Hypothesis.

Deane

Quote from Deane F
"Nothing could be more arbitrary or semantic than mathematics. It is arbitrary because it exists only inside the heads of human beings..."
What on earth do you mean?
Steve D

SteveD --

I think Deane's taking a stance on the old chestnut "Does mathematics have an objective, independent reality or is it merely a cultural/social construct of the human mind?"

Cheers,

Tim
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Os nid Campagnolo yw hi, dyw hi ddim yn werth ei marcho...

Aaaah...suddenly, it's all much clearer...

Cheers,

Tim
_____________________________

Os nid Campagnolo yw hi, dyw hi ddim yn werth ei marcho...

quote:

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Originally posted by Deane F:

Nothing could be more arbitrary or semantic than mathematics. It is arbitrary because it exists only inside the heads of human beings and semantic because it derives meaning in the same way. Prime numbers are just a consensus among people practicing mathematics.

Good luck with the Riemann Hypothesis.

Deane

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But it also has a lot to say about the “real” world. Godel’s theorem is my favourite (although probably not a very good ) example.
I find it fascinating that mathematical models can predict the behaviour of the physical world so well – it makes me think that there is some underlying “truth” in mathematics that goes beyond it just existing in the heads of humans.

Simon

i still have nightmares over the fluid dynamic lectures where the professor would cover an entire blackboard with one partial diffferential equation....

It probably is an old chestnut but most things are in philosophy. Mathematics is a useful tool but it is just a tool. It is a language with no redundancies so it is precise where precision is needed.

"I think Deane's taking a stance on the old chestnut "Does mathematics have an objective, independent reality or is it merely a cultural/social construct of the human mind?""

I wouldn't say "merely", but it is a cultural/social construct. But then, it could be argued that everything is, which would eventually cause my original statement to collapse back to solipsism if I tried to defend it. Occam's razor helps me to keep the entire cosmos from being included in every statement but puts me in a spot of bother when I'm making a proposition about a thinking tool such as mathematics, which is so universally used that (like logic) it's assumed that the world simply works that way.

Mathematics is an abstract system of symbols sufficiently complex to express arithmetic so, just like Godel said, it will be possible to make statements using that system of symbols that will be neither proveable nor disproveable given the rules of that system - like the mathematical possibility that a sphere can be divided into three parts' and then two spheres, each of equal volume to the original sphere, can be made using those parts. I'd like to see that in the real world.

Deane

quote:

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Originally posted by justiceklopper:
i still have nightmares over the fluid dynamic lectures where the professor would cover an entire blackboard with one partial diffferential equation....

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justiceklopper

Has chaos theory simplified the modelling of turbulence in fluid dynamics?

Deane

Quote:-

I think Deane's taking a stance on the old chestnut "Does mathematics have an objective, independent reality or is it merely a cultural/social construct of the human mind?"
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I have a first in Maths but realistically havn't used it in real life.

Regards


NB

Bugger a first, has anyone ever
needed to divide fractions in real life?

Bob

At 1 with the universe

The universe is the way it is. Some of us think we understand some aspects of it....

Maths helps us describe some of its features to one another and helps us predict the outcome of certain events. Sometimes quite accurately, sometimes not.

It is also part of our language, just like words, which help us express ideas and emotions

Maths, language and writing are fundamentally abstract, human inventions, but nevertheless, incredibly useful.

Whether 1 is a prime or not is almost irrelevant and virtually semantic.

"a number that is only divisible by itself and 1"

Our invention of words excludes the number 1, otherwise we would have tortollogy

Of course we could extend the definition with either "including 1 itself" or "excluding 1 itself".

n! + 1 = a prime (but doesn't generate all the primes and doesn't "prove" whether 1 is a prime or not)

Now, allow me to invite you to the "brain teaser" thread to see whether anyone can explain why n! + 1 = prime (and BTW, this would then demonstrate that there are an infinite of primes....

Cheers

Don

has anyone ever needed to divide fractions in real life?

Bob,

you have obviously never had children...."you three can share half this cake between you..."

Mind you, if I read Charles Clark correctly, having a first in maths AND having the amount of experience described above, should qualify you, and ENTITLE (pun intended) you, to be a high court judge or prime minister.

And judging by the present incumbant in the latter role, i'd say he has a point.

cheers

Don

quote:

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you three can share half this cake between you...

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They still have a third each though. In this case a third = a sixth.

Bob
Great post(s)

In this case a third = a sixth.

BigH47,

I have a feeling you could scare Prince Charles rigid......

cheers

Don

quote:

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Originally posted by Martin D:
http://www.utm.edu/research/primes/gifs/gammadef.gif

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I was going to ask, "Well, what i want to know is, how did you get those symbols?" but having just quoted them I've found out.

Kevin

quote:

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Originally posted by Don Atkinson:

Our invention of words excludes the number 1, otherwise we would have tortollogy

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There is an obscure legal pun in there somewhere Don. I haven't found it yet but I'm working on it. I feel I have a duty of care to find it....

Deane,

...I feel I have a duty of care to ....

correct my spelling of tautology......

Cheers

Don

Don,

quote:

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..I feel I have a duty of care to ....
correct my spelling of tautology......

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And here I was thinking you really meant to say tartology, the study of tarts -- whether the pastry or the "honey in a miniskirt" variety I'll leave up to you.

Joe

Joe,

Is there also a pieology?

Dan

Deane,

There is an obscure legal pun in there somewhere Don. I haven't found it yet but I'm working on it. I feel I have a duty of care to find it....

he!he!....the penny just dropped....better go back to school....now, would that be taughtology?

Cheers

Don

Dan,

quote:

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Is there also a pieology?

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Mmmmmmmmm, pi.



Joe