Where does the universe end?

[SlyReaper]

Heh, I like that actually. I never thought of that, Pi has no pattern, As a perfect circle really doesnt exist?

Agh, you're missing the point entirely. It was supposed to be an absurd example to compare to the "why represent a number in two ways" thing. The answer to the pi thing is that a perfect circle DOES exist as a concept. It's a line with constant radius of curvature if you must define it rigorously.

Just like 0.9r exists as a concept. Just like 1 exists as a concept, and which happens to hold the same value as 0.9r.

Pi has no pattern because it's an irrational number. In fact, it's a transcendental number. So for any finite sequence of digits you can think of, the decimal expansion of pi will contain it somewhere.

 

[Hitman_Leon]

You're not allowed to apply logic, the maths bods don't like it

Logic says you are right but maths says you are wrong, because the r is infinite there is no end to guage the difference between 1 and 9r. If you took 9r-1 the number would be 0.0r or so many zero's after the . you would never get to the 1 at the end because there is no end.

I see where you come from, like 1-0.99999 = 0.00001, this can be written as it is a finite and has an end to the squence of numbers but with the infinite recurring number you can't write 0.00000 to infinity the sequence has no end and cannot be noted. If you could get to the end of an infinitly reccuring number that would not be logical and the number would not be infinite it would simply be a number to so many decimal places. Because you cannot reach the end of an infinite number maths uses assumption in the way the number is used and written. So as you cannot write .9-infinity it is written 9r and because you cannot ever reach the end of 9r as it is infinite you could say that assumption rounds up the number for convienience and to make the number useable in maths.

So as a finish, Gilly you are right in logic but maths has to drop logic to make some numbers useable, its not that maths bods drop logic to confuse the layman its that logic cannot always be applied because the answer would be impossible and therefore illogical, so using logic will not always give you logical answers.

 

[SkeeterUK]

It ends at Universe City.

 

[wannabedamned]

I've just been looking at something that's totally blown my mind...

If 1 = A straight line.

And .9r Is a curve bending towards the straight line.

Infinity dictates it will touch it eventually






The fact this blew my mind, could just indicate I know little about the subject and I am still learning

 

[BloodyL]

Great thread guys, really helpful as I'm reading Brian Cox's "Why does e=mc2?" at the moment.
I love how much more ordered it all becomes when you erase the notion of space and time as seperate entities, and realise that without space, there can be no time and vice versa, thus, there really is nothing outside the big bang phenomenon as there wouldn't be any time for any other space to exist in.
Brilliant.

 

[Jonners]

42nd street

 

[SlyReaper]

Logic says you are right but maths says you are wrong

This sentence alone stirs up so much nerd rage in me it's unbelievable. Logic is a SUBSET of maths. The maths says he is wrong, therefore, logic says he is wrong.

Let's take it from the top.

Let x = 0.9r

10x = 9.9r (this is a valid step because when you multiply a number by 10, then every digit in the decimal expansion takes the value of the digit which was previously to its right, and the number of digits after the decimal point reduce by 1. More rigorously, 10 x 0.abcde = a.bcde. But 0.9r has an infinite number of digits after the decimal point, so subtracting 1 doesn't do anything. Thus 10 x 0.9r = 9.9r. QED)

So 10x - x = 9.9r - 0.9r = 9

So 9x = 9

So x = 1

Please tell me where logic has a problem with that.

 

[Hitman_Leon]

Logic has no problem with that, cool your nerd rage lol.

Right, non maths laymen see 9r as an incomplete whole and therefore different 1 as to laymen 1 is 'THE' whole, they dont see the maths behind it as in the example above so seeing 9r a less than 1 is logical to the layman, you dig?

 

[Gilly]

Logic says you are right but maths says you are wrong

...and that's all I've ever said

 

[daz]

The way I look at it is
0.9r = 1 in maths

However in real life 0.9r does not equal 1.

What do you mean "in real life". Since you're talking about numbers, the only realm in which they exist is maths.

 

[daz]

Guys. All you have to do to prove they are different is to find a number between 0.9r and 1.

Shouldn't take too long. Hop to it.

 

[Hitman_Leon]

Guys. All you have to do to prove they are different is to find a number between 0.9r and 1.

Shouldn't take too long. Hop to it.

And while they are at it you should get them to disprove infinity, and bring back beer for everyone waiting.

 

[SlyReaper]

Logic has no problem with that, cool your nerd rage lol.

Right, non maths laymen see 9r as an incomplete whole and therefore different 1 as to laymen 1 is 'THE' whole, they dont see the maths behind it as in the example above so seeing 9r a less than 1 is logical to the layman, you dig?

Ah, I see. You're using some new definition of the word "logic" that I was previously unaware of.

 

[wannabedamned]

Ah, I see. You're using some new definition of the word "logic" that I was previously unaware of.

Reasonable Judgement?

Surely it's reasonable to judge 1 and 0.9r as different considerin they don't look that same?

 

[daz]

Reasonable Judgement?

Surely it's reasonable to judge 1 and 0.9r as different considerin they don't look that same?

You're right, 1/2 isn't the same as 0.5 either. It's just an approximation.

 

[SlyReaper]

Reasonable Judgement?

Surely it's reasonable to judge 1 and 0.9r as different considerin they don't look that same?

Reasonable judgement is not logic. Logic is "The formal systematic study of the principles of valid inference and correct reasoning". I suppose I can concede that for a layman, it would be "reasonable" to judge 0.9r as different to 1. At least, it would be reasonable if you weren't presented with a variety of watertight reasons that they are not different and still remain unconvinced?

 

[SlyReaper]

You're right, 1/2 isn't the same as 0.5 either. It's just an approximation.

 

[Hitman_Leon]

Ah, I see. You're using some new definition of the word "logic" that I was previously unaware of.

So you are unaware of common sense, do you really have to be so tied to the rules of maths as to totally disregard that which is the most basic logic 'common sense' and not understand that the non maths layman see's .9r as less than 1, I know they are the same number but the layman see's it differently.

 

[SlyReaper]

Common sense is not logic. They don't even intersect very often. When it comes to maths and logic, "common sense" and "reasonable judgement" and "intuition" will often lead you astray. This is one of those times.

 

[Hitman_Leon]

Another grey area where the debate would never end, just like 9r, look it dose not hurt to leave the layman with his view and common sense is the logic of life, not the logic of maths and differs to reasonable judgement or intuition, so now do we have to go on, im sure we could discuss examples until death but we wont solve anything.