What is the natural log of zero?

-inf, a valid number.

taks

Just don't bring limits into this discussion now... *shudders*

-inf, a valid number.

taks

<{POST_SNAPBACK}>

 

Which infinity do you have in mind? N0 or N1 or some other? :D

From http://mathworld.wolfram.com/Aleph-0.html comes:

 

"The set theory symbol N0 refers to a set having the same cardinal number as the "small" infinite set of integers. The symbol N0 is often pronounced "aleph-null" rather than "aleph-zero," probably because Null is the word for "zero" in Georg Cantor's native language of German. It is sometimes also pronounced "aleph-zero" or "aleph-naught," the latter of which is also spelled "aleph-nought."

 

The algebraic numbers also belong to N0. Rather surprising properties satisfied by N0 include

 

(1) N0^r = N0 for r>0

(2) r*N0 = N0 for r not 0

(3) N0 + F = N0

 

where F is any finite set. However,

 

(4) N0^N0 = c

 

where c is the continuum.

 

Renteln and Dundes (2005) give the following humorous mathematical analog of the "99 bottles of beer on the wall" drinking song, which refers to its property that : "Aleph-null bottles of beer on the wall, Aleph-null bottles of beer, Take one down, and pass it around, Aleph-null bottles of beer on the wall" (repeat). "

Edited September 12, 200619 yr by Colrom

From http://mathworld.wolfram.com/Aleph-1.html comes

 

"N1 Aleph-1 is the set theory symbol for the smallest infinite set larger than N0 (Aleph-0), which in turn is equal to the cardinality of the set of countable ordinal numbers.

 

The continuum hypothesis asserts that N1=c , where c is the cardinality of the "large" infinite set of real numbers (called the continuum in set theory). However, the truth of the continuum hypothesis depends on the version of set theory you are using and so is undecidable.

 

Curiously enough, n-dimensional space has the same number of points © as one-dimensional space, or any finite interval of one-dimensional space (a line segment), as was first recognized by Georg Cantor . "

Finally, from http://mathworld.wolfram.com/Continuum.html comes:

 

"The term "continuum" has (at least) two distinct technical meanings in mathematics.

 

The first is a compact connected metric space (Kuratowski 1968; Lewis 1983, pp. 361-394; Nadler 1992; Prajs and Charatonik).

 

The second is the nondenumerable set of real numbers, denoted c. The continuum c satisfies

 

(1) N0 + c = c

 

and

 

(2) c^n = c

 

where N0 is aleph0 (Aleph-0) and n is a positive integer. It is also true that

 

(3) x^N0 = c

 

for x>or=2. However,

 

(4) c^c = G

 

is a set larger than the continuum. Paradoxically, there are exactly as many points, c, on a line (or line segment) as in a plane, a three-dimensional space, or finite hyperspace, since all these sets can be put into a one-to-one correspondence with each other.

 

The continuum hypothesis, first proposed by Georg Cantor , holds that the cardinal number of the continuum is the same as that of aleph1. The surprising truth is that this proposition is undecidable, since neither it nor its converse contradicts the tenets of set theory. "

Edited September 12, 200619 yr by Colrom

Finally, regarding division by zero please read the following: http://mathworld.wolfram.com/DivisionbyZero.html .

 

Some aspects of the issue involve complex numbers and are a bit ..... well ...... complex. :D

I said no limits, arrr

 

suppressed... memories... of calculus... coming back.. haunting

dividing by zero is a legitimate function unless the dividend is also zero.

<{POST_SNAPBACK}>

1200-year-old problem 'easy'

Schoolchildren from Caversham have become the first to learn a brand new theory that dividing by zero is possible using a new number - 'nullity'. But the suggestion has left many mathematicians cold.

...

Dr Anderson has come up with a theory that proposes a new number - 'nullity' - which sits outside the conventional number line (stretching from negative infinity, through zero, to positive infinity).

 

clickie!

 

⇐ Pythagoras

It's funny how different our brains work .. math is like gibberish to me.. although I have no problem recongnizing patterns and systems in symbols or number sequences..

 

My brain just go numb when I see these equations.. :crazy:

I don't descry your meaning. Can anyone really descrive it?

Edited December 8, 200619 yr by Blank

You'll need to watch the video accompaniments to descry the full working; perhaps that will help you descrive it better ..?

dividing by zero is a legitimate function unless the dividend is also zero.

<{POST_SNAPBACK}>

1200-year-old problem 'easy'

Schoolchildren from Caversham have become the first to learn a brand new theory that dividing by zero is possible using a new number - 'nullity'. But the suggestion has left many mathematicians cold.

...

Dr Anderson has come up with a theory that proposes a new number - 'nullity' - which sits outside the conventional number line (stretching from negative infinity, through zero, to positive infinity).

 

clickie!

 

⇐ Pythagoras

<{POST_SNAPBACK}>

His paper (PDF) is more informative than 2 video clips on BBC.

Dividing by zero equals death by crucifiction?!?

 

Oh n0es!1

His paper (PDF) is more informative than 2 video clips on BBC.

<{POST_SNAPBACK}>

I see he has redfined some existing axioms:

[A11] Subtraction of Infinity from Infinity ∞