Official TSR Mathematical Society

Chaoslord

now take a number, say 1 for arguments sack. any number divided by infinity produces an infinate number of minute fractions. we can consider this is two ways, the first is if these numbers are very small, if you we can add them all back together, say we had divided 1 by infinty, the sum should be 1, however the sum of an infinate number of minute fractions no matter how minute becomes infinity =], the other is considering the fractions to small to consider, then they add to zero =]

You can have plenty of infinite series that sum to a value other than zero or infinity, e.g. 1 + 1/2 + 1/4 + 1/8 + ... = 2

You haven't got the faintest clue what you are talking about.

Reply 583

73337

18

Chaoslord

agreed but this debate will lead to someone using ***** paradox (wooo i get to)

take normal distribution, probabilities of all possible outcomes can be calculated, some are .0000 in the table you get for S1 but we know its just a very tiny fraction (as you say). (point one)

now take a number, say 1 for arguments sack. any number divided by infinity produces an infinate number of minute fractions. we can consider this is two ways, the first is if these numbers are very small, if you we can add them all back together, say we had divided 1 by infinty, the sum should be 1, however the sum of an infinate number of minute fractions no matter how minute becomes infinity =], the other is considering the fractions to small to consider, then they add to zero =]

hence no matter how small the fraction or how large the fraction, as there can be an argumentative infinite number of real life events, the probability of all of them will be so near zero they must not be considered. if however you wish to consider it you must admit the chances of it happening was impossible for arguments sake. as if i said the chance of you winning was 1 x 10^infinity any statician would say thats pretty much impossible

agreed, bad phrasing sorry =P

though prehaps if you believed in the constant implode explode argument of the universe and the experiment was "time" itself and the only possible outcome is the end of time then no, theres no outcome, as time simply "restarts" after the implosion, theres no end, or begining of time. though thats only if i understand this theory right, which im sure i dont xD

Its not that they add up to infinty its just that it would take an infinite amount of terms to get to a finite number.

Reply 584

Chaoslord

16

Speleo

You can have plenty of infinite series that sum to a value other than zero or infinity, e.g. 1 + 1/2 + 1/4 + 1/8 + ... = 2

You haven't got the faintest clue what you are talking about.

i havent got the faitest clue?

seems a bit rude to be honest. considering i do. :biggrin:

i dont wanna start a heated argument were someone takes it the wrong way because someone says something like "omg your a ******" =P

i said take a number and divide by infinity, i said nothing about a series, now if the sum of that series is 2, then 1/2^infinity was considered and is a real number correct? and has a value, therefore the sum of an infinate number of those, equal infinity, as x times infinity = infinity.

so if i take 1 and divide by infinity, i 1/inifinty. times it by infinity again, considering the fact that you take it as a real tangable number (from your series) it will equal infinity.

dont be rude to people you dont know.

futher proof (the more simple version you may find easier to understand)

according to this, they are the same number, hence the tine franction is not considerate. the tiny fraction can be written as

\frac{1}{infty}

hence.

1 \div {infinty} = \frac{1}{infty}

hence

\frac{1}{infty} \times {infty} = 0

hence i have a clue what im talking about ^^

Reply 585

No you really don't. You can't just multiply and divide by infinity like that.

\frac{1}{\infty} \times \infty

is undefined.

Reply 586

Chewwy

17

Chaoslord

i havent got the faitest clue?

seems a bit rude to be honest. considering i do. :biggrin:

i dont wanna start a heated argument were someone takes it the wrong way because someone says something like "omg your a ******" =P

i said take a number and divide by infinity, i said nothing about a series, now if the sum of that series is 2, then 1/2^infinity was considered and is a real number correct? and has a value, therefore the sum of an infinate number of those, equal infinity, as x times infinity = infinity.

so if i take 1 and divide by infinity, i 1/inifinty. times it by infinity again, considering the fact that you take it as a real tangable number (from your series) it will equal infinity.

dont be rude to people you dont know.

futher proof (the more simple version you may find easier to understand)

according to this, they are the same number, hence the tine franction is not considerate. the tiny fraction can be written as

\frac{1}{infty}

hence.

1 \div {infinty} = \frac{1}{infty}

hence

\frac{1}{infty} \times {infty} = 0

hence i have a clue what im talking about ^^

this is the most idiotic **** i have ever seen.

Reply 587

harr

harr

This reminds me of part of HHGTTG where Adams "proves" that the population of the universe is zero. He doesn't use the same concept, but they both involve the idea of a probability which is as close to zero as to almost make no difference.

Reading some more of my posts I've changed my mind. Basically the same argument is being used, not a different one. For anyone interested, Adams' argument goes as follows:

"It is known that there are an infinite number of worlds, simply because there is an infinite amount of space for them to be in. However, not every one of them is inhabited. Therefore, there must be a finite number of inhabited worlds. Any finite number divided by infinity is as near to nothing as makes no odds, so the average population of all the planets in the universe can be said to be zero. From this it follows that the population of the whole universe is also zero."

You can't just do all that division and multiplication by infinity.¹ Infinity is much more complicated than that.

Edit: Typo.

Reply 588

nota bene

If what is being done is

\lim_{n\to\infty}[\frac{1}{n}]\times\lim_{n\to\infty}[n]

then it should be okay to say it is 1, but otherwise it is impossible to deal with infinity as a normal number.

Reply 589

100% Mathmo

Hey can I join up to this society. I'm in Yr 12 and although some of this is a bit over me i would like to know as much as i can!

Reply 590

*Anneka

11

100% Mathmo

Hey can I join up to this society. I'm in Yr 12 and although some of this is a bit over me i would like to know as much as i can!

but I'm more worried because I'm starting maths at uni this year! lol

Reply 591

Donar

Good morning. Going to start with some maths at OU next September.
May I join?

Reply 592

Only once you have completed the three sacred challenges of the Official TSR Mathematical Society. Do you have the intelligence, the perseverance and the courage to undertake the first of your three challenges? You may still walk away now, but once you have accepted there is no turning back.

Reply 593

Chaoslord

16

this infinity business seems to have caused alot of outrage, well tbh, its all opininated. all the cant divide then times thing, i dont agree, i was told every number system has a set of rules like a.b = b.a or a + b = b + a, there are a set of concepts which are used, im not sure what they're called though.

and if infinity doesnt follow the rule, its not part of the number system, which would make a large chunk of maths not real... yea we can argue all day but theres no point, theres no right or wrong answer, this concept of infinty has been argued for years

but the ideas which have been raised are realy good, i like harrs thing about a population of zero xD but its the same concept, dont be narrow minded and simply say "your wrong", just because this theory tests your knowledge and makes you think out side the box doesnt mean its wrong, remeber everyone said the world was flat, but guess what, its its realy a cube (just jokin)

btw what are the three tasks?

Reply 594

You are a very annoying person.

You can't just refute what mathematicians have proven and known for centuries (i.e. that

\frac{\infty}{\infty}

is undefined) with no proof of your own except a couple of garbled paragraphs of nonsense. The truth of a mathematical statement is not dependent on the opinion of a random 17 year old.

Reply 595

harr

Chaoslord

i was told every number system has a set of rules like a.b = b.a or a + b = b + a, there are a set of concepts which are used, im not sure what they're called though.

Axioms.

and if infinity doesnt follow the rule, its not part of the number system, which would make a large chunk of maths not real...

To quote wikipedia (maybe not the most accurate source, but it wll do) "in mathematics "infinity" is often used in contexts where it is treated as if it were a number (i.e., it counts or measures things: "an infinite number of terms") but it is a different type of "number" than the integers or reals."

Reply 596

I don't think the commutativity of addition and multiplication are actually axioms but that's the word you're looking for (there is a high probability that I am wrong).

harr please edit out that last sentence I want to have some fun :frown:

Reply 597

RichE

Speleo

I don't think the commutativity of addition and multiplication are actually axioms but that's the word you're looking for (there is a high probability that I am wrong).

They're part of the axioms of the real number system - or going back from that you may define all numbers in terms of sets and these "axioms" would then be theorems, but they'd be based on axioms assumed about sets (e.g. the ZF axioms).

Reply 598

Thanks. I've been wondering, is there one fundamental set of axioms shared by most (all?) branches of mathematics, or does each area have it's own set of axioms that cannot be derived from any more fundamental ones?

Reply 599

RichE