Sunday, March 15, 2015

2/0 = (i*i)?

In mathematics, division by zero is division where the divisor (denominator) is zero. Such a division can be formally expressed as a/0 where a is the dividend (numerator). In ordinary arithmetic, the expression has no meaning, as there is no number which, multiplied by 0, gives a (assuming a≠0), and so division by zero is undefined. Since any number multiplied by zero is zero, the expression 0/0 has no defined value and is called an indeterminate form. Historically, one of the earliest recorded references to the mathematical impossibility of assigning a value to a/0 is contained in George Berkeley's criticism of infinitesimal calculus in The Analyst ("ghosts of departed quantities").

There are mathematical structures in which a/0 is defined for some a (see Riemann sphere, real projective line, and section 4 for examples); however, such structures cannot (see below) satisfy every ordinary rule of arithmetic (the field axioms).

In computing, a program error may result from an attempt to divide by zero. Depending on the programming environment and the type of number (e.g. floating point, integer) being divided by zero, it may generate positive or negative infinity by the IEEE 754 floating point standard, generate an exception, generate an error message, cause the program to terminate, or result in a special not-a-number value.

21 comments:

FreeThinke said...

I must confess a sorry fact.
I comprehend not the Abstract.
And though today it is the fashion,
I have for it no hint of passion.
If you think this makes me stupid,
I might just concur with you, kid.


(:-o

-FJ said...

:0

Gert said...

Any number divided by 0 equals infinity. Subtraction means finding out how many times you can subtract the divisor (denominator) from the numerator before obtaining 0, e.g. 8/4 = 2 because you can subtract 4 from 8 two times before hitting 0.

(With a any number) a/0 = infinity because you can subtract 0 from a an infinite number of times and still not obtain 0.

i is the conventional notation for the imaginary number i which is the square root of - 1 (minus 1). i *i can be 'reworked' as i^2 (i squared) and equals - 1.

Obviously 2/0 = - 1 is a fallacy!

Lyin' Brian said...

Yes 2/0 = -1 is a fallacy...

But then, "infinity" is not a number, either. And an "imaginary" number requires an "imaginary unit". I contend that the solution to the problem 2/0 would require an "imaginary unit" as well... such as "infinity". Yet at the same time, the "resulting" products of currently designated "imaginary numbers" are negative. ;)

Lyin' Brian said...

...call the negative a "dimensional belt twist" to correct for it's appearance out of another dimension.

Lyin' Brian said...

:P

Lyin' Brian said...

aka - its' quantuum entanglement.

FreeThinke said...

THe age old cry of the uniniiated:


AAAAAAAAAAAAAAAAAAAAAAAAARGH!!

-FJ said...

It's all just idle speculation to accompany the subject of the song, FT. And in my case, pure b.s. ;)

nicrap said...

One of my high school teachers taught me this:

a^2-a^2 = (a+a) (a-a) (Difference of squares formula)

a(a-a) = (a+a) (a-a)

a = a+a

a = 2a

1 = 2

neat, eh? ;)

-FJ said...

So?

Plato, "Parmenides" - One is not many, and therefore has no parts, and therefore is not a whole, which is a sum of parts, and therefore has neither beginning, middle, nor end, and is therefore unlimited, and therefore formless, being neither round nor straight, for neither round nor straight can be defined without assuming that they have parts; and therefore is not in place, whether in another which would encircle and touch the one at many points; or in itself, because that which is self-containing is also contained, and therefore not one but two.

:P

-FJ said...

One is the "unit". It isn't a number. It takes a "two" to create a "one" which is now also a member of the set of "number".

-FJ said...

But then "number" has no existence either... Plato, "Parmenides" - Thus, one, as being the same and not the same with itself and others—for both these reasons and for either of them—is also like and unlike itself and the others. Again, how far can one touch itself and the others? As existing in others, it touches the others; and as existing in itself, touches only itself. But from another point of view, that which touches another must be next in order of place; one, therefore, must be next in order of place to itself, and would therefore be two, and in two places. But one cannot be two, and therefore cannot be in contact with itself. Nor again can one touch the other. Two objects are required to make one contact; three objects make two contacts; and all the objects in the world, if placed in a series, would have as many contacts as there are objects, less one. But if one only exists, and not two, there is no contact. And the others, being other than one, have no part in one, and therefore none in number, and therefore two has no existence, and therefore there is no contact. For all which reasons, one has and has not contact with itself and the others.

nicrap said...

AAAAAAAAAAAAAAAAAAAAAAAAARGH!! ;)

Gert said...

nicrap:

Neat but fallacious, of course. To get from from line 2 to line 3, one (no pun intended!) is dividing both sides by 0 (a - a), creating an indeterminate. No wonder one 'ends up' with 1 = 2, LOL.

It's like saying something times zero = something else times zero, ergo something equals something else. Not on! ;-)

Neatest identity in the knowable universe:

e^(Pi*i) + 1 = 0

-FJ said...

Very neat those transcendental numbers... :)

-FJ said...

from Wolfram: Transcendental numbers are important in the history of mathematics because their investigation provided the first proof that circle squaring, one of the geometric problems of antiquity that had baffled mathematicians for more than 2000 years was, in fact, insoluble. Specifically, in order for a number to be produced by a geometric construction using the ancient Greek rules, it must be either rational or a very special kind of algebraic number known as a Euclidean number. Because the number pi is transcendental, the construction cannot be done according to the Greek rules.

Gert said...

Transcendental numbers rock. And e is one of the most important ones, without exponential functions our world would fly apart: even atoms could not exist without them. e^f(x,y,z) provides the 'damping' that makes electrons bound to the nuclei, without it you've got particle soup.

BTW, I tested Wolfram's ability to solve differential equations and was positively surprised. It's even syntactically quite forgiving. Impressive, even though I haven't put it through its paces yet. 'Expert systems' are the eay to go but how they would fit into petit bourgeois free marketism, I'm not entirely sure.

nicrap said...

It's like saying something times zero = something else times zero, ergo something equals something else. Not on! ;-)

Bang on! ;)

-FJ said...

how they would fit into petit bourgeois free marketism...

The same way "Microsoft" does. Charge "rent" on the general/commons through "intellectual property" laws. Government becomes the new "enforcer" of "intellectual property rights". Liberalism 5.0

Gert said...

Yeah, I read the one about rent already. See also how Windows 8 now seems essentially to have become an app store and how users of Office will be made to pay subscription fees, on a product where initial development costs have already been recovered a million times over!