how long is infinity?, I once read this desciption of infinity and I quote, although not quite verbatim

If you imagine the earth is actually a huge ball bearing made of steel, ok, and once every million years a fly lands on it and flies straight away again, when the earth has been worn away, infinity will not even have started


thoughts please

Originally posted by brandnewdrunk

thoughts please

Take more water with it.

Nomme

Isn't it like a figure eight that fell over?

Infinity isn't a number, it's a concept, we need it to make maths work.

That strangest thing is, infinity is also a mathmatical impossibilty, well as near as it can get in world of lies, damn lies and statistics.

Wilf

How can it make maths work if it don't have any value?

It's just a get-out-clause for mathematicians to give a name to something they don't understand.

Mark my words.

zero has no value, yet it is vital to even mental arithmetic.

infinity is likewise, a container or a set, rather than a fixed value.

infinity has no size, cannot be added to or taken away from.

the ability to detect infinite recurrence, as well as infinite recursion , in a process or function, is one of things that still separates our minds from computers.

Yes, I get your drift: infinity +1 = 1

zero + 1 =1

Am I getting near?

Originally posted by Sam Miguel
Yes, I get your drift: infinity +1 = 1

zero + 1 =1

Am I getting near?

No.

Infinity is a concept not a number. It is the way to explain the fact that the sequence of numbers we use is never ending. Therefore adding 1 to infinity is a non-sense because, obviously, infinity isn't a finite number to which you can add. Zero on the other hand, while in some respects still being a concept, still holds a single finite value, so adding 1 to a zero value would indeed be 1.

Thanks . T. It's a bit like doing the age-old sum of multiplying loads of numbers and putting a zero somewhere in the middle.

A table without a fruitbowl full of apples standing on it is completely different to a an identical table without a fruitbowl full of oranges or apples.

So: A full lift is different to a full lift, as is an empty lift and so on.
And an empty lift is a full lift?

Well, dig me parrot's head up please!

my favourite definition of infinity is that it's like washing up - You think that you've washed every darn pot in the house but there's ALWAYS another cup! Works with most other kinds of housework too...

Originally posted by Sam Miguel
Yes, I get your drift: infinity +1 = 1

zero + 1 =1

Am I getting near?

nope. way off.

I simply said that infinity, like zero, has no value, yet it was useful in maths. Merely because a concept has no numerical value does not mean it is useless in maths, as you implied.


infinity as a concept in mathematical terms (as I understand it with my limited knowledge of maths), it is the nirvana state that calculations like "1/3" approach in the recurring decimal at the end. No matter how long you carry on carrying the one and dividing by three you get the same answer. For ever and ever.

No one can count to infinity, but numbers can progress towards it, just like the recurring number in 1/3, but also in pi, the golden ratio (phi), fractals and so on. It is a final frontier, the eschatology of arithmetic.

It's interesting that the natural constants like pi have this never ending quality to them - in that they continue to yield information and accuracy the farther you calculate them.

Phan you mention fractals.

Fractal can't really be tarred with the same brush as infinity.

infinity is a concept

fractals are repeating equations that can never end, they cannot be explained numerically very well but they really show off thier beauty when represented graphically.

You get some pretty pictures from fractals, but it is hard to show without some pretty nifty resolution and graphics program.

Wilf

Yes, I get your drift: infinity +1 = 1

zero + 1 =1

Am I getting near?

Afraid not...

infinity + 1 = infinity

zero + 1 = 1

infinity - 1 = infinty

infinity *-1 = -infinity

Its a complex concept to understand, but very useful in almost every aspect of physics and serious maths (the one with the letters instead of numbers).

If you want a literal way of thinking of infinity this is quite a nice (if not mathematically precise answer):

There is a hotel with an infinite number of rooms. You arrive late one night and ask the front desk clerk if they have a vacancy. He replies that every room is occupied, however, he can arrange for you to get one. But how, you wonder, if there is no vacancy?

The answer is simple: the clerk will simply ask the people in room 1 to move to room 2, those in room 2 to move to room 3, those in 3 to move to room 4, and so on. Since there is an infinite number of rooms, everyone will have a room to move into, and room 1 will be available for you.

Just as your given you your key, an infinite number of people arrive at the hotel. The clerk cleverly figured out how to get you a room, but can he accommodate an additional infinity of guests? Amazingly, he can. He just asks everyone to move again, but this time to the room number that is twice the number of their current room. In other words, you would move to room 2, the people in 2 would move to 4, those in 3 to 6, those in 4 to 8, and so on. This will leave all odd numbered rooms — an infinite number of them — vacant.



This has a lot to do with set logic and infinite set logic.... just thoight I'd illustrate!

Another interesting (IMHO) way of looking at it:

"Nicholas of Cusa (1401-1464) made the following interesting point regarding the shape of an infinite circle. The curvature of a circle's circumference decreases as the size of the circle increases. For example, the curvature of the earth's surface is so negligible that it appears flat. The limit of decrease in curvature is a straight line. "

An infinite circle is therefore... a straight line!

useful????


Probably not :)

Computers can represent infinity ... it's called:

Divide By Zero *crash* !!

Originally posted by Ow-Zone
... infinity *-1 = -infinity ...

How can there be a '-infinity' !? ... now that is MAD.

Originally posted by Ow-Zone

"Nicholas of Cusa (1401-1464) made the following interesting point regarding the shape of an infinite circle. The curvature of a circle's circumference decreases as the size of the circle increases. For example, the curvature of the earth's surface is so negligible that it appears flat. The limit of decrease in curvature is a straight line. "

An infinite circle is therefore... a straight line!

useful????


Probably not :)

You really cleared that one up Ow-Zone!

But is that intellectualism for intellectualist sake?

For if old Nicky Cusa had have had the opportunity of flight, he would have seen for himself that it is a big line, but definately not straight.

Hot air balloons not developed until the late 18th century, so unless he was good at climbing mountains....

venger, while this is true, you have to bear in mind that even if a method for viewing the earth from greater distance was known it wouldn't stop this from being true.

Infinity would also seem to curve if seen from a point not on the line, our perceptions make this happen and over accentuate the curve.

How often do we seen things that aren't there? or not see things that are. I think that this is why our mathematics is also flawed. The only numbers/concepts that should be accepted as a standard mathematic base are pi, infinity, i and e.

the only reason we work to base 10 is because we have ten fingers. How different would mathematics be if we had 6 fingers?

Pi, infinity, i and e are all numbers/concepts that are vital to any understanding of what is going on around us. For example, if we were visited by a sentient alien species these 4 numbers/concepts would likely be our common ground on mathematics, not the number 1, or even 42 (heh).

Wilf

Originally posted by BrainThrust


Infinity would also seem to curve if seen from a point not on the line, our perceptions make this happen and over accentuate the curve.

Wilf

If we are to use a straight line as a model to represent infinity, (eg: thin beam of light) in a pseudo contained space like a moniitor, and all around the coloured beam of light was blackness.

How else could you perform this experiment or a similar?

Our basic understandings of perspective would not trick us in to thinking that the light was curved. We would not know for sure, but the reduction in size over distance would not appear to be curved. That is presuming that us as spectator remained static.

Using math is another method entirely to demonstrate the theory as you well know.

I was only commenting on the quote posted by Ow-Zone which is about 600 years old mind.

What is 'e' anyway? (In mathmatics, I don't want any drug related answers).

E is a difficult one to explain.

It is the exponential growth number.

for example:

x^e=y

if you put this as a graph then you would get the natural growth curve for anything. It is kinda difficult to explain but it is one of the most vital numbers when biology turns to mathematics.

Wilf

Originally posted by BrainThrust
Pi, infinity, i and e are all numbers/concepts that are vital to any understanding of what is going on around us.

e^(i pi) = -1

That made my brain hurt :loopy:

Simple answer??…as Rowan Atkinson once said – ‘infinity is a sod of a long time’…enough said!!

Originally posted by Sidla
What is 'e' anyway? (In mathmatics, I don't want any drug related answers).

OK, you asked for it!

e is appoximately equal to 2.71828

You have a graph y = e^x, ( i.e. at each point on the graph you take the x coordinate and and do e to the power of x to find the y coordinate)

Then at each point on the curve, the slope of that curve will be equal to the y coordinate (which also equals e^x).

The graph y=e^x is the only one where this is true.

In mathspeek, if y=e^x, dy/dx = e^x..

It's related to biology, and radioactive decay and such things:

If the rate of change of population growth is proportional to the current population, then you could say:

dP = k * P * dt
(dP=change in population, dt=change in time, k=arbitary constant)

you can rearrange this and integrate it to give

ln P= k*t
(ln P is the natural logarithm of P, the inverse of e^P)

So, this is the same as

P = e^(k*t)

(Some minor points and factors ignored to reduce confusion!)

ant.

That much I understand, Ant, but I don't understand how
e ^ (i*pi) = -1

That was the point where I had to give up understanding the reason for somthing, and just accept that it happens because it happens. It's a beautiful equation though, in its own way.

This tread > my brain can handle on a sunday morning.

Originally posted by Andy
That much I understand, Ant, but I don't understand how
e ^ (i*pi) = -1

That was the point where I had to give up understanding the reason for somthing, and just accept that it happens because it happens. It's a beautiful equation though, in its own way.
Just put that into my maths simulator and you're right. I don't understand why either. :confused:

When I left school there was no such thing as the square root of a negative number. When I went back to do maths for my degree several years (no not decades) later there was. How strange was that? My whole bedrock shaken.:confused:

Originally posted by max
When I left school there was no such thing as the square root of a negative number. When I went back to do maths for my degree several years (no not decades) later there was. How strange was that? My whole bedrock shaken.:confused:
There's no such thing in 'real' terms. Sqrt(-1) is a complex number. It can only exist on an imaginary axis.

Consider this: 7y + minus not 7y does not automatically negate itself and become a foolish sum. There is no actual balance - but it is a perfectly legitimate sum.

If you look at the evidence:

It is sound. The statement stands up for itself.

7y + minus not 7y = ?

Answers on a postscard please!

Originally posted by Andy
That much I understand, Ant, but I don't understand how
e ^ (i*pi) = -1

That was the point where I had to give up understanding the reason for somthing, and just accept that it happens because it happens. It's a beautiful equation though, in its own way.

Well, there are several ways of trying to understand this. This one probably isn't very satisfactory but anyway...

The function e^x can be expanded to the folowing infinite sum:
(1) e^x = 1 + x + x^2/2! + x^3/3! + ....

and therefore
(2) e^(ix) = 1 + ix - x^2/2! - ix^3/3! + x^4/4! + ix^5/5! - ...

the function sin(x) expands as
(3) sin(x) = x - x^3/3! + x^5/5! - ...

similarly,
(4) cos(x) = 1 - x^2/2! + x^4/4! - ...

Therefore looking at equation (4) and (3) and (2), you can see
(5) cos(x) + i*sin(x) = e^(ix)

Put x = pi into equation (5), and use cos(pi) = -1 and sin(pi) = 0 and you see that...

(6) e^(i*Pi) = -1

Ant.

Originally posted by Phanerothyme
zero has no value, yet it is vital to even mental arithmetic.


Really?
The Romans seemed to manage OK without it. Accoding to this page the concept of 'zero' didn't 'appear' until 1000AD.
http://www.legionxxiv.org/numerals/


Oh, and as a side note some infinities are bigger than others.

Nomme

The Romans, however, never mastered intergration, differentation or astronomy (to any accuracy)... the arabs however did so very well (given the technology availavble) they aslo had a number system with a zero.

It's twice the distance from the middle to the end.

Alternatively it's what is at the end of the counting.