Things you don't need to know…

If you ask Siri to divide by zero, this is what she would say (though I've heard she doesn't do it anymore.)

Originally Posted by Eye
As you all know the beard is back - pity if you ask me.

THEN I WON'T ASK YOU, OK?

Eh… Sorry about that.

Nevertheless, the history of the beard is quite interesting:
Beards, Past and Present.

The "Piccadilly Weepers", or "Mutton chops", are awful to see but best to kiss if you ask me, no distracting crumbs or tickling hairs.
My favourite: "La mouche"/"A la royale", because somehow I always assume the man wearing it is well-mannered.
Most fascinating: Mesopotamian beard style.

Interesting. Mine is a combination of the Egyptian and the Greek style.

pibbur who still won't ask the eye who doesn't look like an eye anything. Even kisses. Or hugs. The wife's coming home today after spending two days in Copenhagen visiting graveyards.

Originally Posted by pibbur who
The wife's coming home to day after spending two days in Copenhagen visiting graveyards.

Graveyards? O dear, what on earth is she up to?

Edit: changed the avatar. Eyish enough for you?

She's working at the graveyard authority (don't know if that's the right word) here in Bergen. Administration, not digging.

pibbur who likes the new avatar of the eye, but who admits she can choose any avatar she wants to.

[QUOTE=Ripper;1061415063]If you ask Siri to divide by zero, this is what she would say (though I've heard she doesn't do it anymore.)
…
Funny. Unlike google whic does nothing if you ask it to calculate 0/0 (or 7/0, any number/0).

But what is 0/0? 1? Zero? Infinity. Informally, we can say that the answer is all of them. Well, actually we can't say that something is infinity, but 0/0 would match any number we chose. So it's undeterminate.

There is an excellent numberphile video here. covering x/0, 0/0 and also 0^0 and why you can't say that something like x/0 is infinity.



Then we have this one, among other things covering why it's make sense to define 0!=1.


Than we have pathetic things like this, where some amateur tries to prove that you can devide by zero, despite what mathematicians say.

Among the things he does wrong is to assume that you can devide by zero, and use that to prove that you can do it. And that he uses infinity as a regular number.

pibbur who plans to study a lot more mathematics when he retires. Why? Because it's fun!!!

Originally Posted by Hurls
Wabbit season!!!

Kangawoo season!!!

Pibbbur who wonders when it's koawa season.

PS. Did you know that you can configuwe Googwe to use Ewmew Fudd as wanguage? Along with Klingon, Pirate and Bork! Bork! Bork! Sadly not Sindarinf, Quenya or Blackspeech. PS.

Yes, the other day someone asked what the Watch was worth, and I attempted to show that its value is undetermined, since the answer must be x divided by the membership price (zero). The Watch seemed unmoved by my theorem.

Case (1)
Let be x <> 0

Lets assume a definite number y exist, that

x/0 = y

then y*0 must be x.

But y*0 is always 0. x = y*0 = 0.
A contradiction to our precondition x <> 0.


Case (2)
Let be x = 0

Lets assume a definite number y exist, that

x/0 = 0/0 = y
Then y*0 = 0.
But this is true fo every y.
A contradiction to our precondition that y is a definite number.

Ergo:
y= x/0 is not defined

And for the question whether x/0 is infinity or not:

We cold use limits and demonstrate that y/x->infinity as x->0. But this assumes that x >0. Because if x<0 we get y/x->- infinty as x->0. Therefore we cannot say that y/0 is infinity, instead x/y approaches (we can make |x/y| as large as we want) + or - inifnity depending on whether x> or x<0.

pibbur who has an upper limit to the number of quarks and electrons in his body.

Now for a quick question: Why do we define 1 as not prime? It surely isn't divisible by any integer value other than itself.

pibbur who knows the answer (and he's not talking about 42).

Originally Posted by Ripper
Yes, the other day someone asked what the Watch was worth, and I attempted to show that its value is undetermined, since the answer must be x divided by the membership price (zero). The Watch seemed unmoved by my theorem.

Nitpicking: x/0 is undefined, not undetermined. There is a subtle difference between those two terms.

Assume 1/0=y exists. Then we have 1=0*y. There is no value of y that multiplied by 0 equals 1. Therefore x/0 is undefined.

On the other hand, using a similar argument for 0/0=y. Then as HiddenX pointed out 0=0*y, which holds for any value of y. So 0/0 is undetermined.

pibbur who thinks he's both defined and determined.

Infinity is a fairly troublesome concept in itself, and is also not well-defined, as it means slightly different things in different cases. Some infinities can be shown to be larger than others, for example.

A number of philosophers and mathematicians are not happy about this sort of thing, but most people just shut up and calculate.

Originally Posted by Ripper
Infinity is a fairly troublesome concept in itself, and is also not well-defined, as it means slightly different things in different cases. Some infinities can be shown to be larger than others, for example.

Yep, there is the question of whether an infinite set is countable or not. In a countable set, every element can be associated with one integer. The set of integers is of course countable. So is the set of all even numbers. Or numbers divisible by 7. And the set of rational numbers (fractions). All of these are of the same cardinality (one way of saying that their "equally large").

But the set of real numbers (pi, e,square root of 2…) can be shown to be not countable and therefore of a higher cardinality.

But it is to some degree a question of how we define things.

A number of philosophers and mathematicians are not happy about this sort of thing, but most people just shut up and calculate.

Interesting.

pibbur who insists that the set P={pibbur} is countable. He will however not be held accountable for what he writes.

PS.
For those confused by number sets, here are the important sets, each of them includes the above mentioned sets.

N is the set of natural numbers, integers > 0.

Z is the set of postive and negative integers and 0. The set includes N

Q is the set of rational numbers, positve or negative fractions. The set includes Z

R is the set of real numbers, whch includes the rational numbers and numbers like pi, e and so on. Every number that can be represented on a number line belongs to R. Other numbers do not belong to R, those belong to the next set, the complec numbers.

C is the complex numbes, of the form a+b*i, where a and b are real numbers and i (for imaginary number) is the square root of -1. i is not a real number, since no real number satisfies x^2=-1. C contains R, we get R by setting b=0.
DS.

Edit: Corrected a nasty typo. Complex numbers are of the form a+b*i, not a=b*i, which doesn't make sense. *shivers*

Originally Posted by pibbur who
Now for a quick question: Why do we define 1 as not prime? It surely isn't divisible by any integer value other than itself.

pibbur who knows the answer (and he's not talking about 42).

Well, nobody came up with an answer, so here it is.

We could (and we did for a long time) consider 1 a prime. But if we do, we're making things a bit more complicated than necessary.

One example, the fundamental theorem of arithmetic which says: Every integer >1 is either a prime, or a unique product of primes. As the name suggests, this is a very important theorem in mathematics.

We have for instance 42=7*3*2. No other product of primes give this number (sorting the factors differently doesn't count). Now, if 1 is prime we would also get:

42=7*3*2*1
42=7*3*2*1*1

and so on. This invalidates the uniqueness part of the theorem.

We could solve this by reformulating the theorem: Every integer >1 is either a prime, or a unique product of primes larger than 1. But there are many other theorems where we would have to do the same. So, the most practical solution is to exclude 1 from the set of primes. After all 1 is a very special number with fundamental properties not shared by primes >=2.

Among those we have:

1. a*1=a, which actually is one of the fundamental axioms (multiplicative identity axiom) defining the set of integers (and the rational, the real and the complex).
2. a*b=1, which is one of the axioms defining the rational numbers (the reals and complex as well), the existence of the multiplicative inverse.

Observe that 2) does not hold for integers.

Now for another question about primes. 2,3,5,7,11,13,17,19,23,29,31,37 are all primes, they come up quite often in the example (the primes in integers< 40). Now, is there a sequence of 1 000 000 consecutive numbers where none of them is a prime? If so, how to prove it?

pibbur who doesn't think "which number has the unique prime product 2*3*7?" is the question.

1000000!+2 … 1000000!+1000000
gives you 1000000-1 numbers that are not prime.

by definition n! is divisible by all numbers from 1…n
and

n!+2 is divisible by 2
n!+3 is divisible by 3
…
n!+n is divisible by n

Exactly! (not the faculty)

This also means that there is an infinite sequence of consecutive numbers where none is prime. And of course, being countable, this sequence is just as large as all the integers.

pibbur who, being divisible by for instance b (giving piur), is not prime, although being the only one, is the prime of pibburs.

Originally Posted by pibbur who
Observe that 2) does not hold for integers.

Unless both a and b are 1.

Gah! Go away with your maths.
I know the rule of three …

Originally Posted by Jaz
Gah! Go away with your maths.
I know the rule of three …

Then what three numbers give the same result when added or multiplied?

Originally Posted by Jaz
Gah! Go away with your maths

This is what happens when someone divides by zero. I blame myself.