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Deeper than primes

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doronshadmi said:
On the contrary. Traditional Math lacks the computational skills to comprehend the following equation: 0.999...[base 10]+ 0.000...1[base 10]=1
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That idea have been handled so it would accommodate cases other than the one you used explicitly. Just check out an example.

limit_division_tan_and_x.gif


The symbol x → 0 replaces your 0.000...1.

Now solve (0.999...)/(0.000...1) = x.
 
punshhh said:
I'm not a mathematician, but even I can see that this is wrong.
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Really?

So, what do you get if you divide 1 by 3, then multiply by 3?

What do you get if you subtract .99999... from 1?

Doron is simply pointing out how something finite can arise from a singularity.
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No, Doron simply points out his own lack of understanding.

A point in a singularity is infinitely small and infinitely numerous. In order to pull the points apart to form 3 dimensional space a gap or line must be placed between the point/s. This line has and consists of relative quality.
By quality I mean an attribute or quality which is different from singularity.
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I have no idea what you're trying to say.
 
punshhh said:
I'm not a mathematician, but even I can see that this is wrong. Have you not heard of infinite regress?
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Yes, most of us have. It's you who has absolutely no idea what it is and how it proves the very point you are arguing against.

punshhh said:
Doron is simply pointing out how something finite can arise from a singularity.

A point in a singularity is infinitely small and infinitely numerous. In order to pull the points apart to form 3 dimensional space a gap or line must be placed between the point/s. This line has and consists of relative quality.
By quality I mean an attribute or quality which is different from singularity.
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Inane drivel.
 
zooterkin said:
Really?

So, what do you get if you divide 1 by 3, then multiply by 3?

What do you get if you subtract .99999... from 1?
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The source of confusion is the mixing of exact and approximate numerical formats and insufficient definition of the terms in question. Dividing integers such as 1 and 3 can take on various forms. The result can appear as an irreducible fraction 1/3 (exact format) or you can use an algorithm called "the long division," stick it into an infinite loop and watch a never-ending array of threes:

1 LD 3 => .333333333333333333333333333333333333333... (approximate format)

The idea that 1/3 = 0.333... is wrong as much as EXACT=APPOXIMATE is wrong, but it is harmless in practical computations. The fraction 1/3 is basically the limit of 1 LD 3; it is a hypothetical value that 1 LD 3 = 0.333... never reaches, but comes "infinitely close to." Since most of the numerical and symbolic operations require the usage of the exact format, limits are used and so 1/3 * 3 = 1. But 1 LD 3 * 3 = 0.999... The practical difference between 1 and 0.999... is something only Doron is capable of worrying about.
 
punshhh said:
Please explain how this is the case.
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Explain? To you? Do you think I'm some kind of masochist? I assure you, I'm not. I have no illusions anymore about you being able or not to learn.

Ask someone who is not yet fed up with your nonsense. Read zooterkin's post. Or epix's post. It's in there.

ETA: Oh, and to top it off, you're dishonest too, as the arguments against materialism thread showed.
 
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punshhh said:
A point in a singularity is infinitely small and infinitely numerous.
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A point is exactly the smallest possible element.

A line segment is "at its best" an ever smaller element, that logically can't be reduced into the smallest possible element.

This reasoning is consistent, straightforward and easily understood by any opened mind.

The reasoning that can't get that is used by persons that do not have an opened mind, which is the majority of the current community of pure mathematicians, which has no clue about the real complexity of the co-existence of the ever smaller AND the smallest.
 
epix said:
The practical difference between 1 and 0.999... is something only Doron is capable of worrying about.
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If one wishes to deal with real complexity, he\she simply can't ignore the difference among the ever smaller and the smallest.
 
doronshadmi said:
0.999...[base 10]/ 0.000...1[base 10] = ∞[base 10]
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The expression "∞[base 10]" is the smoking gun: you really treat infinity as a number. There is enough elementary and very informal stuff on the net to exorcise the devil out of your head, but only if you want to get rid of it.

What is infinity?

Infinity is not a number; it is the name for a concept. Most people have sort of an intuitive idea of what infinity is - it's a quantity that's bigger than any number. This is sort of correct, but it depends on the context in which you're using the concept of infinity (see below).

There are no numbers bigger than infinity, but that does not mean that infinity is the biggest number, because it's not a number at all. For the same reason, infinity is neither even nor odd. [continues...]
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http://mathforum.org/dr.math/faq/faq.large.numbers.html

Since infinity is not a number, the math folks must adjust the terms for handling the same question I asked you. Here is the answer:

[lim x → 0](1 - x)/x = ∞

The above says that as x is approaching zero, ∞ is the limit of f(x) = (1 - x)/x. That means f(x) grows unbound in a divergent manner. The usage of "infinity is the limit" is very unfortunate, coz it may imply that infinity is a number or a point on the real line that cannot be reached by any sequence or a function.

Read up a bit on the abbreviated history of infinity.
http://en.wikipedia.org/wiki/Infinity
 
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zooterkin said:
So infinity in base 2 is five times as big as infinity in base 10?
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Yes.

EDIT:

Yet there is a bijection between the number of "0" symbols, which represent the locations along "0.000...1[base 2]" and "0.000...1[base 10]" expressions, upon infinitely many different scale levels.
 
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laca said:
Yes, most of us have. It's you who has absolutely no idea what it is and how it proves the very point you are arguing against.



Inane drivel.
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Really laca, science tells us that all the atoms (points) where present in one point (singularity), at or slightly before the Planck epoc during the big bang.

We have a vast quantity of atoms in the universe, nearly infinite in number. Perhaps these atoms or their precursors were nearly infinitely small at this point of time.

During the period of inflation presumably these atoms (points) somehow moved apart to form 3 dimensional space, they moved from nearly infinitely small to just small.

This “small” is the qualitative or relative aspect (line segment), the size (quality) of which is clearly finite as opposed to nearly or wholly infinite.

Without this relative finite small space between and defining the size of these atoms they could not have emerged from that nearly infinite point.
 
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punshhh said:
Really laca, science tells us that all the atoms (points) where present in one point (singularity), at or slightly before the Plank epoc during the big bang.
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"Atom" is one of many terms Doron uses with no regard to their actual meanings. It is certainly not being used in this thread by anyone in the sense of a physical particle, nor are we discussing the Big Bang. You seem to be going off on a tangent entirely of your own.

(You might want to check that your keyboard is working, you seem to be losing characters. (Planck, epoch, for example.))
 
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