Thank you Johnnie, my son,. I do have the best course on Quantum Mechanics from The Teaching Company, and I also have the video's from Berkeley. So, I can probably understand it as well as any other person whom has taught advanced Math and Physics.

It's the observations and the claimed puzzlements that I think point to a lack of understanding with our conventional math and methods of analysis.

Daddio,
If you feel that your teachers are explaining it properly to you, and you understand it, then stick with it, that's good.

It took me almost 2 years to find someone who explained it properly. Now i know all the other people where "winging it" without really understanding it.

John.

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I don't think that this set of affairs and Godel's work prohibit us from ultimately understanding anything at all.

But, no matter how much we and our tools evolve, we will always be finite beings with a finite capacity of understanding...
So, understanding anything at all wont be possible unless the "underlying reality" (not the perceived reality) is finite in their very own nature.

And worst, even if the reality were finite, knowing everything at all, imply that we have been able to proove the inexistence of everything else not included in that knowledge, but "everything else" it's not a (and will never be) a finite set...

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What did God do before creation?

Try asking him for I see no reason why he should not tell you.

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The Kite Fliers

--------------------
Kite fliers: An imaginary club of solo members, those who don't yet
belong to a formal team so "fly their own kites" - as the saying goes.

In order for 3 times .3333333.... to be equal to 1.000000.... the two numbers would have to agree in a very large number of instances. These agree in none whatsoever.

It seems to me that 3 * (1 / 3) = 1, so the issue here appears to be whether (1 / 3) = 0.333333.... (or could it be whether 1 = 1.000000....?). If you believe that (1 / 3) = 0.333333...., then surely it follows that 3 x 0.333333.... = 1? If you don't believe (1 / 3) = 0.333333..., what does (1 / 3) = ?

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I think you'll find it's a bit more complicated than that ...

sigh .........

1/3 is a fraction. To convert that to base 10 decimal the answer is 0.33333..... recurring, an approximation. There is no direct equivalent. You are trying to combine two number systems.

sigh .... ;-)

The .... indicates recurring to infinity.

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I think you'll find it's a bit more complicated than that ...

You are correct, but purists would use a dot or line over the first decimal figure. But of course you would never be that picky ... ;-))

My question about the equality or otherwise of 1/3 and 0.333333.... was to William Rothamel, I'll wait for his answer.

While waiting, and seeing as you have time on your hands, maybe you could answer what is 1 - 0.999999....?

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I think you'll find it's a bit more complicated than that ...

Bobby, IIRC .333333333333.................. is supposed to mean on to infinity which would be 1/3. I do admit that is something from about 50 years ago so maybe something has changed in math or, LOL dementia is setting in.

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sigh .........

1/3 is a fraction. To convert that to base 10 decimal the answer is 0.33333..... recurring, an approximation. There is no direct equivalent. You are trying to combine two number systems.

We've been down this road before. And, as I said, barring any discussion of hyper-reals, indeed 1/3 = 0.3 (repeating 3), i.e. 0.333... .

To say it is combining two number systems would thus reject 1/2 = 0.5, but I doubt anyone has any problem with that one, eh?

You are correct, but purists would use a dot or line over the first decimal figure. But of course you would never be that picky ... ;-))

I would, but both are accepted conventions and, short of embedding a pic or maybe ... maybe looking up an arcane bbcode, the ellipsis is preferable,

You are correct, but purists would use a dot or line over the first decimal figure. But of course you would never be that picky ... ;-))

My question about the equality or otherwise of 1/3 and 0.333333.... was to William Rothamel, I'll wait for his answer.

While waiting, and seeing as you have time on your hands, maybe you could answer what is 1 - 0.999999....?

No, betreger, nothing has changed, but William wants to bring in another, currently nonstandard view, the hyperreals.
From the standard view, the equalities Bobby and I state ae correct.
And if Chris does not want to answer, I'll wait precisely 0 seconds before giving bobby my version of the answer. :)

There are those here who do not believe that:

(infinity) * 1 / (infinity) = 1

is a true statement.

This because an application of the associative and communicative laws results in:

{1 / (infinity)} + {1 / (infinity)} + {1 / (infinity)} {repeated (infinity) times} = 1

If they were to believe that, then any positive probability for the universe and given an infinity of time results in certainty that the universe arose from random chance.

Of course in Algebra we are taught that: A * 1/A = 1. There is no special magic by replacing A by (infinity).

So in answer to the question: What did God do before creation? He waited for the right random number sequence? He rigged it so we can't answer the question? He created himself with time?

There is no satisfactory answer to the question.

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There are those here who do not believe that:

(infinity) * 1 / (infinity) = 1

is a true statement.

This because an application of the associative and communicative laws results in:

{1 / (infinity)} + {1 / (infinity)} + {1 / (infinity)} {repeated (infinity) times} = 1

If they were to believe that, then any positive probability for the universe and given an infinity of time results in certainty that the universe arose from random chance.

Of course in Algebra we are taught that: A * 1/A = 1. There is no special magic by replacing A by (infinity).

So in answer to the question: What did God do before creation? He waited for the right random number sequence? He rigged it so we can't answer the question? He created himself with time?

There is no satisfactory answer to the question.

With A=0 the equation falls down. I suspect that the mathematicians here can show why the same is true with A=(infinity).

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I think you'll find it's a bit more complicated than that ...

There are those here who do not believe that:

(infinity) * 1 / (infinity) = 1

is a true statement.

This because an application of the associative and communicative laws results in:

{1 / (infinity)} + {1 / (infinity)} + {1 / (infinity)} {repeated (infinity) times} = 1

If they were to believe that, then any positive probability for the universe and given an infinity of time results in certainty that the universe arose from random chance.

Of course in Algebra we are taught that: A * 1/A = 1. There is no special magic by replacing A by (infinity).

I dont believe it because I know that infinity/infinity its not equal to 1.

It happens that Infinity its not necessarily equal to infinity. (there are infinite points in a line, there are infinite points in a plane, and its not hard to see that there should be more points in a plane than in a line... thats because the number of points in the plane is an infinite of a higher order of magnitude than the number of points in the line (and my wording its not fully right as there are no such thing as the "number of points in a line" because the set of points that belongs to a line is a not an enumerable set).

infinity / infinity, 0 * infinity, 1/0, 0/0 and 1/infinity are undeterminated values and the result of such operations can only be solved using limits and knowing the function that gives the "infinity" or "zero" value.

You can say that the limit when n tends to infinity of n/n is equal to 1
But, the limit when n tends to infinity of n/n^2 (which is also infinity/infinity) equals 0... Take out the magic word "limit" and you will get that 0 = infinity/infinity = 1 => 0=1!! Avada Kedabra!

(I just hope that all this makes sense in english... Ive learned maths in spanish, and learned english mostly reading things on internet, so its highly probable that Im not using the right "technical" words...)

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There are those here who do not believe that:

(infinity) * 1 / (infinity) = 1

is a true statement.

This because an application of the associative and communicative laws results in:

{1 / (infinity)} + {1 / (infinity)} + {1 / (infinity)} {repeated (infinity) times} = 1

If they were to believe that, then any positive probability for the universe and given an infinity of time results in certainty that the universe arose from random chance.

Of course in Algebra we are taught that: A * 1/A = 1. There is no special magic by replacing A by (infinity).

I dont believe it because I know that infinity/infinity its not equal to 1.

It happens that Infinity its not necessarily equal to infinity. (there are infinite points in a line, there are infinite points in a plane, and its not hard to see that there should be more points in a plane than in a line... thats because the number of points in the plane is an infinite of a higher order of magnitude than the number of points in the line (and my wording its not fully right as there are no such thing as the "number of points in a line" because the set of points that belongs to a line is a not an enumerable set).

infinity / infinity, 0 * infinity, 1/0, 0/0 and 1/infinity are undeterminated values and the result of such operations can only be solved using limits and knowing the function that gives the "infinity" or "zero" value.

You can say that the limit when n tends to infinity of n/n is equal to 1
But, the limit when n tends to infinity of n/n^2 (which is also infinity/infinity) equals 0... Take out the magic word "limit" and you will get that 0 = infinity/infinity = 1 => 0=1!! Avada Kedabra!

(I just hope that all this makes sense in english... Ive learned maths in spanish, and learned english mostly reading things on internet, so its highly probable that Im not using the right "technical" words...)

c^2 = c.
If you want something larger than c, you need the cardinality of the power set of the reals, for example.

My question about the equality or otherwise of 1/3 and 0.333333.... was to William Rothamel, I'll wait for his answer.

While waiting, and seeing as you have time on your hands, maybe you could answer what is 1 - 0.999999....?

Oooh me espies a chink in the mighty ones armour :-)

1 - 0.99999 recurring is 0.00001 with the last zero recurring, I would have thought. And even if it isn't, what does it matter in the scheme of things. In terms of God and maths, we all know the answer is 42 anyway.

Always got time to chat to you Bobby, everyone needs their litle bit of amusement for the day.

Solve for x, 10x - x = 9.

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I think you'll find it's a bit more complicated than that ...

ROFL...

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The Kite Fliers

--------------------
Kite fliers: An imaginary club of solo members, those who don't yet
belong to a formal team so "fly their own kites" - as the saying goes.

Very amusing, was 10x - x = 9 so difficult?

10x - x = 9 => x(10 - 1) = 9 => 9x = 9 => 9x/9 = 9/9 => x = 1

agreed?

Now let's try substituting 0.999999... for x and see what happens:

(10 x 0.999999...) - 0.999999... = ?

10 x 0.999999... = 9.999999...

x = 1 | x = 0.999999...
10x   |   9.999999...
- x   | - 0.999999...
= 9   | = 9.000000...

oh dear, if x = 0.999999..., then 10x - x = 9, though we just showed that when 10x - x = 9 is solved for x, x is 1, thus 0.999999... = 1, so 1 - 0.999999... = 0, just like Sarge hinted at.

Where was that chink?

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I think you'll find it's a bit more complicated than that ...

1 - 0.999999... = 0, just like Sarge hinted at.

Where was that chink?

Indeed.

What was god doing before the creation? Laying down the groundwork for Maths, so that once the creation was finished, the "many" can be bamboozled by the "few".

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What was god doing before the creation? Laying down the groundwork for Maths, so that once the creation was finished, the "many" can be bamboozled by the "few".

No bamboozling.