unforum

[thebruce]

[thebruce]

here's a link to one nice little thread where the guy sends in a few words what I've been saying...
http://www.labgoats.com/ads/view.php?idtag=2449&responses=12

another interesting thread...
http://www.tacalumni.org/article.php?story=20040109214003133#comments

[yanka]

[Chris K]

So infinite series can't have exact finite sums?

Look at this triangle:



It's equilatrial.
I think you would agree that the angle is exactly 30 and the section at the bottom is exactly 0.5

That 0.5 was calculated with an infinite series!

Here it is (I don't know why you want it):


There you go.
Infinite series can can can can can have exact finite sums.

Do you want me to show you more parts of mathmatics and physics that fall apart if you don't believe that?

That last paragraph of yours makes me feel ill.
You have no idea what you are talking about.

EDIT__________________

You can't say that decimals are simpler or more accurate than fractions!

And can you please stop saying 'infinite numbers' when you mean recurring / irrational / transendental

[tanner]

tanner's adaptation of Chaitin's constant:

which gives the probability that for any set of posts, a universal forum machine will halt, where p is the number of members in the forum.

this number is not only irrational and transcendental but also unthinkable

[firefox]

[thebruce]

[Chris K]

For god's sake!
Just give it up!!!

You said earlier that you had just never seen an infinite series give a finite sum.

I just showed you that you can.

All you need to know is that sin is calculated by adding up an infinite amount of numbers that get smaller and smaller, but - for 30 deg - it comes out at exactly 0.5

I'm sorry, you clearly have no idea what you are talking about.

Some of the stuff you have said is just so ridiculous I can't even comprehend it.

Just accept that the sum of an infinite amount of numbers can exactly equal a 'normal' (irrational) number.

This:

[thebruce]

[Chris K]

I don't think you know what an infinite series is.

A repeating number isn't an infinite series. It's a number.

An infinite series is a series of numbers not a series of digits.

0.123123123123123123 <== not an infinite series
1 + 1/2 + 1/4 + 1/8 + 1/16 .... <== an infinite series

Therefore, you don't know what you are talking about.

----------

[thebruce]

[neon snake]

thebruce,

I'm still keen before moving much further to have a definitive list of the points you disagree with/interpret differently to us. Reason being, the points we seem to disagree on are changing.

For example the statement - 'in an infinitely long string of random digits, the probability of any possible finite string being found is 100%.' - seems to have divided us - I say its 100%, you say its both 100% and 0%.

We then moved on to various discussions whether there is such a thing as an infinite series, or an infinite string, and how you can only prove a string or series is infinite by calculating all the possible values (?), around recurring decimals, representing fractions in decimal notation, and numbers like pi and e, where representing them in decimal requires a rounding at some point. Various people have voiced opinions, proofs and facts, and I'm starting to lose track of which bits you agree with, and which you don't. And indeed, what we're discussing, as we keep moving the goalposts.

I'd like a list, so that we can be a bit more constructive in where we're going.


Incidently, I had a look at the links you posted - helped me pass a very boring afternoon at work.

Some of the argument (and it was as difficult to track as this thread) seemed to revolve around the following-

1 divided by 3 is 0.3recurring - in decimal notation.

0.3recurring multiplied by 3 is 0.9recurring - in decimal notation.


Therefore maths is broken (or words to that effect, but spread over a couple of days worth of posts).

This is incorrect.

1 divided by 3 is one third. In decimal notation we say 0.3recurring, because there exists no other way to write it.


However, 0.3recurring multiplied by 3 IS NOT 0.9recurring - its 1 (exactly 1).

The only way you get to 0.9recurring is to multipy each of the 3s in the string by 3. The problem lies here.

If you do that, then you have ignored the recurring part of the number, and have just multiplied 0.3 by 3, and then added the recurring part back on afterwards.

Try it on a calculator (NOT IN EXCEL). You'll get 1 divided by 3 =0.333333333.

Now multiply by 3. You'll get 0.999999999. This is because the calculator works out 0.3recurring to a set number of decimal places, but can't handle true recurrence.

Now try in excel, which is better at maths than a calculator, and can handle true recurrence, understands that it's a mere representation, and gives an exact value of 1! Magic.

[Chris K]

I really don't have the energy for this.

You clearly have little knowledge of fairly simple mathmatics or even mathmatical language and notation.

Rest assured, that if you keep adding up these terms:

1 + 0.8 + 0.64 + 0.512 + 0.4096 ...

where every term is 0.8 times the one before, to infinity, you will come to exactly 5.

If you can't accept that then you can't accept trigonometry or calculus.

------------------

- Sin of a number is calculated by adding up an infinite number of numbers.
- The result is often a rational number

Sin is not some kind of 'look-up' function.

If you want to find out the length of the side marked x in this picture:


Then add up all of these terms:

1 - 1/6 + 1/120 - 1/5040 + 1/362880 - 1/39916800 ......

[ustice]

Real quick. Not getting in to an argument, but I love this example.

take a line (its easier to illustrate) and assign it a langth of 1 membit (fake unit)

________________________________


now split it in half
________________ ________________

now we have 1/2 + 1/2 membits = 1 membit

split the right one in half
________________ ________ ________

now we have 1/2 + 1/4 + 1/4 membits = 1 mmbits

split again
________________ ________ ____ ____

1/2 + 1/4 + 1/8 + 1/8 = 1 membit

again
________________ ________ ____ __ __

1/2+1/4+1/8+1/16+1/16 = 1 membit

and conntinue...

1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256 + 1/512 + 1/1024 + ... = 1 membit

We are not removing removing anything in our cuts so we KNOW that we have 1 membit total, and yet in this thought experiment we can make an infinate number of cuts. this can be represented by the infinite sum:

OO
----
\ 1
> ------- = 1 membit
/ n
---- 2
n=1


infinite sum giving a finite value.

I love that one, though it is more fun when you start with a square and chop it up as you get the golden spiral, but that is harder to illustrate in text without taking up the entire screen.

Yay math.

[Chris K]