The complement to nothingness need not be its negative nor its contradictory nor its opposite. Nothing might be the inverse of something or the reverse, and both could fit the system at the same time and it could be as much something as anything else. The world of predicate logic is not exclusionary except for binary operations.

Ok, easy. The definite integral from 0 to infinity of e^(-x)*Cos[x]. Plug in the evaluation of the definite integral using integration by parts:1/2(e^(-x)*(Sin[x]-Cos[x])|from 0 to V. Now we do a little algebra plugging in the values for the equation f(v)-f(0) and get: lim as v -> infinity of 1/2[e^(-v)*(Cos[v]-Sin[v]) -(-1)]. Now, as V goes to infinity, e^v does as well, so we have Cos[v]/e^v-Sin[v]/e^v+1. The Cos and Sin terms approach zero as v goes to infinity since a number divided by infinity is zero, so the whole thing is equal to 1/2[0-(-1)] which is equal to 1/2 which is the answer. This is a common calculus problem. It is not simple, but it gives a very simple answer, the ammount of space under this infintely extended function is 1/2. It is the same as half of a unit square on the cartesian plane. This makes sense though. All of the space on the cartesian plane is of infinite density. The plane is an approximation of the syntax of the funcitons applied to it.

Arjen;

Mathematics does not have spatial representation any more than words do, thus there is indeed always a little lost in translation. Mathematics is to pictures as words are. You can describe a scene with words but there will always be somthing lost in translation. Mathematics is useful in a number of ways, but you could not call mathematical logic an error of reason, for it is stand alone and logically sound. An applicatoin of it, depending on the applictaion, might certainly be erroneous, but the system uses tautologies to manipulate mathematical statements and write proofs, in and of it self there is no error.

You take mathematics a necessarily an object with the intent of representing a model of reality, this is not necessarily true. It can model limited aspects of our reality, and it does very good with htese approximations, as far as computer science it does extremely well, as computers are binary systems. I view mathematics as several things at once, and not as a single thing. Godel has shown us that mathematics is disjoint to at least some degree, and I think that the sort of generalization you present is not accurate. Insofar as logic can be used to probe the relational nature between physical objects, mathematics is useful. There are certain boundries we shall and do hit with this. We try to work around them, but mathematics does indeed have its limitations, especially when used improperly.

The number zero is defined as the set of empty sets.

Neither zero nor the empty set is nothing.

See: Introduction to Mathematical Philosophy, (1919), B. Russell.

You are right. They are really something! Aren't they? The empty set is a set with no members.

I'd like to add that originally functions were simply rules to take us from one number to the next via a given rule set, generally one derived from algebra, though it could also be recursive as seen in the cantor set function. It wasn't until later that the idea of functions as graphs came along.

Anyone read Spengler on math? Any one like Nicolas of Cusa? Is it calculus in a roundabout way to call a circle a polygon with an infinite number of sides? Does this idea amuse any else? Nicolas used it as a symbol for God.

Wasn't Zero especially useful as a place-holder first? Zero, infinity, and one. That's quite a menu already.

This is why I love nothing! It changes. If nothing is left alone, it is truly nothing, and the exact time you think of nothing, *poof!* its gone! Or, maybe we can't imagine nothing, because it's perfect!

Zero is supposed to represent nothing. But as soon as you give nothing a name, it turns into something. Therefore zero is not nothing. Zero is something. Nothing is nothing. Get it?

It is false to say that zero is supposed to represent nothing.
Nothing cannot be represented because it does not exist.
There is no property that non-existent things have.
Zero certainly does exist.
Zero has the property of being less than one, therefore zero exists.
Giving nothing a name does not make any difference to the existence of nothing.
Do you really think that because God is a name that therefore God exists???
Nothing is nothing, is a contradiction.

You are correct in saying that nothing does not exist, but in the wrong way. Nothing is the lack of somthing or the relation to somthing, so it cannot exist. By trying to rationalize that for nothing to exist it must be related to somthing, you have made nothing somthing.

Epic fail.

You always have a problem with communicating with people correctly.

Zero is the presence of an absence. A name without a referent that serves as a useful piece in any case. Great symbol, this number zero. It's an egg. It's a hole. It's a snake with its tail in its mouth.

The only other number that matters is 1. (Couldn't we do the same math exclusively in binary code?)

This one is just a vertical line. Like the pronoun "I." Phallic. Like a simplified drawing of a man in the void.

Beckett wrote a book called Worstward Ho. First sentence: "On." On is the Greek word for Being it seems. (Correct me experts if I am wrong.)

1 & 0, Being and Nothingness, Male and Female, Vertical Axis versus Curvaceous Closure.

Alberto Giacometti - Wikipedia, the free encyclopedia

---------- Post added 02-24-2010 at 12:44 AM ----------


Records show that the ancient Greeks seemed unsure about the status of zero as a number. They asked themselves, "How can nothing be something?", leading to philosophical and, by the Medieval period, religious arguments about the nature and existence of zero and the vacuum. The paradoxes of Zeno of Elea depend in large part on the uncertain interpretation of zero.
The concept of zero as a number and not merely a symbol for separation is attributed to India where by the 9th century AD practical calculations were carried out using zero, which was treated like any other number, even in case of division.[9][10] The Indian scholar Pingala (circa 5th-2nd century BC) used binary numbers in the form of short and long syllables (the latter equal in length to two short syllables), making it similar to Morse code.[11][12] He and his contemporary Indian scholars used the Sanskrit word śūnya to refer to zero or void.

Wow, this is something I also believe, and find very significant.

Being and negation are the two fundamental logical-mathematical categories. All else is derivative. It's in the TLP, but it must be assembled from the pieces. For some reason no one usually notices how radical the TLP is. He reduces logic to tautology and negation. Logic says nothing but is a backbone of non-logical meaning. Negation is just the un. A hole that is unthinkable outside its donut but stark naked within it, for us to infer its basic importance to thinking....

The number zero is strange indeed. One is the primary number, the number the system is built on. Zero is a necessary asymmetry. Think about it. We can't divide by it. Adding and subtracting it are a waste. It's there to bridge the one to the fulcrum of the number line. Which could just as easily be flipped from left to right....We could do it all with one operator, but that's not as convenient.

As Frege explains clearly in The Foundations of Arithmetic, to say that the number of apples is 0 is simply to say that there are no apples. The mystery lies in the concept of a number as an object; but this mystery attaches no more to 0 than to any other counting number. What does make 0 special, of course, is that it is a counting number whose name is never uttered during counting! And indeed it took some anonymous Indian genius to invent it (if I remember right). Still, having been invented, it is as easy (and as hard) to account for as any other finite cardinal number. (Sorry if this has already been explained, but it is quite a long thread, and so far I have only read the first couple of pages.)

That's not all of it, Twirlip, as zero is where the negative meets the positive. Zero is the fulcrum of spectrum in that sense, while One is the tempered interval, the core of the thing. The negative and positive are sustained by the one universal operator. We don't need both plus and minus. That's just a convenience. We could double-plus or double-minus....the operator is just a reversal of the placement logarithm. All numbers are created from just one number, and zero allows a symmetrical "negative" realm on the number line...

the original concept of zero was with summerians as an accounting concept

which was to be taken as you zero assets but not to think that the object its self was completely and absolutely eliminated , physically

Is zero the middle of infinity?

zero has nothing to do with infinity

there is no middle to infinity , infinity is what it is

How about zero as the junction of twin, mirror infinities?

Multiplication/division are the proportional operators, right? And subtraction and addition are something else. It seems that most of our natural laws are about proportion and inverse proportion. And when it comes to proportion, one functions as zero does when it comes to addition or subtraction.

So 1/infinity is one boundary of proportion, and infinity/1 is the other. Positive or negative. I think negatives are useful especially on the coordinate plane. Image trying to graph functions without negative numbers. We would lose all kinds of symmetry. How would we get downward and leftward motion?

Zero seems like an infinitely thin boundary between the negative and positive zones, at least in respect to multiplication. With addition, the zones have a different relationship, it seems.

For instance, if you add a negative to a positive, the sum has the sign of the larger added number. But if you multiply a negative and a positive, the product is always negative.