Infinitely small?

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Davidc

Guru
Location
Somerset UK
Archie_tect said:
Pie is delicious and in our house it most certainly is finite.
Pi, on the other hand.... ultimately must have a finite limit otherwise a circle couldn't exist in reality.

I suspect he meant that you can describe in the decimal number system pi to an infinite number of places withour there being a repetitive sequence of digits.

In English - its a surd.
 
OP
OP
Chuffy

Chuffy

Veteran
<peers out from behind sofa>
Have the scary men gone yet? ;)
 

Archie_tect

De Skieven Architek... aka Penfold + Horace
Location
Northumberland
Noodley said:
Ayway, X Factor has just come on. And Robbie is gonna be singing LIVE.
Time to go for a long bath.....

Can Robbie sing?
Shove up I could do with a soak!
 

Archie_tect

De Skieven Architek... aka Penfold + Horace
Location
Northumberland
Once confused a solicitor when she asked whether the car approached the junction, from the right or the left, by saying it depends which way you're looking.
 
snorri said:
....and who started all this?;)

:smile::biggrin:
I've a nasty feeling I did. (get thee behind that sofa Chuffs...)

Pi isn't an infinite number. But it can be expressed as the sum of an infinite series which gets closer and closer, the more terms you add, but never quite reaches it. The best known (and the most inefficient) is Gregory's Series:

Pi/4 = 1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + ......

Go on adding terms in the same manner, alternately adding and subtracting. The result will get closer and closer to pi/4. But you'll never quite get there...
 

Ian H

Ancient randonneur
All you need to do is keep dividing by 2. You can go on for ever but you'll never get to zero.
 

atbman

Veteran
I'm deeply worried about the effect that this discussion is having on the universe.

Since entropy will eventually lead to the heat death of the universe and entropy involves a reduction in the total amount of information in the universe and we are now even more confused, there has, therefore, been an increase in entropy, so the end has been brought nearer.

Therefore:

WILL YOU PLEASE STOP!!!!
 

marinyork

Resting in suspended Animation
Location
Logopolis
It was actually Pete that really started it. I am aware that this kind of discussion can give people a headache so deliberately didn't mention calculus, sets, the continuum hypothesis, transcendental numbers and all that ;).

But just for clarity Pi is not a surd. And strangely enough the territory we've got onto isn't actually that far from removed from whether something in the universe could literally be infinitely small.

So sorry chuffy. So very basically black holes have singularities. This is because you get large amounts of matter in one place, leading to very high gravity which increases and increases and actually warps/destroys space itself it is that powerful!
 
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