Zero & Infinity

"Nothing is bigger than infinity" means "There is no number which is bigger than infinity", the "nothing" there works as a quantifier. It doesn't mean "0" is greater than infinity, since 0 is a particular number.

But there is a 0 relating to the "Nothing is bigger than infinity" statement, equivalently "The size of the set of numbers which is bigger than infinity is 0"!

Quoting fdrake

"Nothing is bigger than infinity" means "There is no number which is bigger than infinity", the "nothing" there works as a quantifier. It doesn't mean "0" is greater than infinity, since 0 is a particular number.

But there is a 0 relating to the "Nothing is bigger than infinity" statement, equivalently "The size of the set of numbers which is bigger than infinity is 0"!

You make complete sense and thank you. In a sense the two zeros involved - the regular (whole number) 0 and the 0 of "...the set of numbers which is bigger than zero..."- are about different things. One is itself a number and the other is aboutnumbers "...bigger than infinity..."

If you'll permit me to pick your brain a bit more, I want to ask a follow up question. I can understand that the zero in "nothing is bigger than infinity" is the cardinality of the set of numbers bigger than infinity. That zero counts the number of elements in the set of numbers bigger than infinity which is zero.

However notice the regular zero, the whole number zero, it represents or even is nothing itself, right? Zero is nothing or do you disagree? If you don't then the problem resurfaces because when I say "nothing is bigger than infinity" I can't be talking about any other number but zero. The literal truth being that there's nothing in "...the set of numbers which is bigger than infinity..."

Forget all I said...I left it there to show you my work, like a good student does. I believe I've figured it out. Zero is the numerical/quantitative property of nothing and isn't quite the concept nothing itself. When I say "nothing is bigger than infinity" I'm talking about the concept nothing and not zero, the number which is the numerical aspect of nothing. Thanks a ton.

@The mods: Kindly delete this thread. It's continued existence is no longer justifiable. Thanks.

Quoting TheMadFool

However notice the regular zero, the whole number zero, it represents or even is nothing itself, right? Zero is nothing or do you disagree? If you don't then the problem resurfaces because when I say "nothing is bigger than infinity" I can't be talking about any other number but zero. The literal truth being that there's nothing in "...the set of numbers which is bigger than infinity..."

You know, there are lots of concepts that a zero can refer to. Not all of the mathematical "ideas" associated with 0 are associated with it being the cardinality of the empty set. And I very much doubt that the philosophical ideas regarding nothing or nothingness are reflected in zero either.

Here's a few "zero ideas" which the cardinality of the empty set doesn't get at directly [hide=*] (but can be proven to derive from it)[/hide].

0's the additive identity. If you add 0 to a number, you don't change the number.
0's what's called a multiplicative annihilator (or an absorbing element), if you multiply something by 0 it turns into 0.

Apparently wikipedia has a list of ways of making things that work like 0!

Reply to fdrake Another issue regarding nothing is that in our discussion I made the remark that zero is the quantitative property of nothing. That just doesn't feel right to me...there's a part of me that says nothing can be said about nothing which, in my book, means it shouldn't possess any properties for properties are what provides the foothold that enables us to, well, speak of things. Nothing isn't, isn't supposed to be, a thing. This doesn't seem to make sense either for if nothing shouldn't/doesn't have any properties, then it can be said to have zero properties and again, math has, in some sense, spoken what should be the unspeakable.

Along the same line, your last post was about the properties of zero (additive identity, multiplicative annihilator, etc) and this totally contradicts our, my, intuition on nothing - it simply can't, rather shouldn't, possess properties for to posses properties is to be something and that leads us to the possible reason why the Greeks, mathematicians par excellence, were deeply troubled by the question,

[quote=The Greeks]How can nothing be something?[/quote]

To the Greeks, zero didn't make sense.

Quoting TheMadFool

To the Greeks, zero didn't make sense.

And here, unfortunately, neither does nothing. :roll:

Quoting jgill

And here, unfortunately, neither does nothing. :roll:

I'm in a bit of a mess right now. Can't seem to wrap my head around something in another thread. Thanks for the comment. Take care and Good day.

Quoting TheMadFool

To the Greeks, zero didn't make sense.

I remember reading somewhere that 0 didn't make a whole lot of sense to Greek mathematicians because they didn't think of magnitudes in the same way. Numerical magnitudes represented ratios of measurable (in principle) objects. You can't measure an object to have 0 size with a straight edge, something with zero size isn't "there" to be measured in the first place.

Though whether this kind of thing is interpretively valid is another question; "what would the Ancient greeks before the invention of zero thought of 0?"

Quoting TheMadFool

contradicts our, my, intuition on nothing - it simply can't, rather shouldn't, possess properties for to posses properties is to be something and that leads us to the possible reason why the Greeks, mathematicians par excellence, were deeply troubled by the question,

What I'm about to say is a throwaway troll comment: nothing is absent properties, you mean nothing is distinguished by the property such that for any other conceivable property it does not hold of nothing?

Regardless, if your "nothing" has no properties, it doesn't relate to the mathematical concept of 0.

One of the important uses of zero is as a place holder; a ten and a unit is distinguished from a hundred and a unit by the insertion of a zero - 11 and 101. In this context it is as fruitful to wonder about zero as it is to wonder about a comma. If you read "Eats, shoots and leaves" you will understand the importance of the comma to meaning, but do not ask what the comma itself means - it means nothing. By which I mean that it has no meaning of itself, but modifies the meaning relation of the words it associates with, depending on its position.

Quoting unenlightened

but do not ask what the comma itself means - it means nothing.

This claim is very suspicious. If a comma doesn't have meaning, then individual letters don't have any meaning either. And if letters don't have meaning then words don't have meaning unless words are a case of creating something from nothing. But I suggest that a comma really does have meaning, just like a letter has meaning, words have meaning, all symbols have meaning, and arrangements of symbols have meaning. Or is it your point that the meaning is in the arrangement, not in the symbol itself?

Reply to fdrake Here's what think. From a set theoretic perspective:

Consider the following set:

List A: {>}, {zero}, {dog}
List B: {a, %}, {9, cat}
List C: {living mammoths}, {x such that x = x + 1}

The numerical abstraction from the sets in list A is one-ness.

The numerical abstraction from the sets in list B is two-ness.

The numerical abstraction from the sets in list C is zero-ness

So far so good.

At this point, I'd like to draw your attention to language, specifically the English language because everbody seems to know English, and look at English from the perspective of your favorite word processor.

Take the sentence, "this is good" and take note of the spaces between the words. Spaces have no meaning in English, at least none like letters and words do. Their function in English to help distinguish individual words and that's about it. Space (in English) is linguistically nothing if only in the sense that they lack meaning similar to letters and words.

From a word processor's point of view it's an entirely different story. Space is treated, like letters and symbols, as a character. Spaces in a word processor take up memory - it's a thing, a something, in the world of a word processor. In other words, nothing has been raised to the status of a letter.

If one, for the sake of argument, regards a word processor's point of view as an abstract nevertheless fully legit theory, it can be said that word-processor-ily nothing is a character as much as "a" or "8" or "#" is.

Let's go back to list C, the empty sets. Each set has no elements which is just another way of saying the sets "contain" nothing. This compares to thinking about nothing at the same level as English views spaces in sentences. When we start to look at space as a character like a word processor, treat nothing as a number in its own right the magic happens.

Nothing is better than heavenly bliss.

But a ham sandwich is better than nothing.

Therefore a ham sandwich is better than heavenly bliss?

Quoting Pfhorrest

Therefore a ham sandwich is better than heavenly bliss?

Depends how you define ham sandwich and heavenly bliss. If heavenly bliss involves never getting to the washroom, because it's such a dirty, unholy thing, then yes, ham sammich is better than all eternity in bliss without a piss.

Reply to TheMadFool
No "thing" bigger than infinity
but
"""""Nothing""""""" is not bigger than infinity
In other words,
the no.of things that are bigger than infinity is zero,but the "nothing" itself (or 0 ) is not bigger than infinity.
The fun fact is that we can use the expression "nothing" to refer to two separate meanings:
1) nothing can mean: zero of things.
2) nothing can also mean: the "nothing" itself ,which in this case is the number 0.
So basically, your misusing of the language lead to the problem you showed.

Reply to TheMadFool
Anything divided by infinity is equal to zero and anything divided by zero is infinite. I've been told that this isn't necessarily true in almost every Math class that I've taken since high school, but I still hold to it. Bernhard Riemann seems to have thought so as well.

Reply to thewonder Any positive number divided by x approaches infinity as x approaches zero (negative numbers instead make it approach negative infinity), and anything divided by x approaches zero as x approaches either infinity or negative infinity.

But when x equals exactly zero, you can’t say whether the ratio equals positive infinity or negative infinity, since it depends on what direction you approached from, therefore division by exactly zero is undefined.

And your x can never reach either positive or negative infinity, because those aren’t actually numbers, so the ratio will never end up equaling exactly zero either.

On this thread, the posts imply nothing is as it seems. :cool:

When you divide by zero, you can say that it is positive infinity. When you divide by positive or negative infinity, you can say that it is zero. That is what I am saying.

Infinity is the limit. It is not the numbers that approach it. Within such a mathematical system, zero could, perhaps, be like a limit as well. I haven't exactly reasoned this all of the way out.

Edit: Zero, I think, would actually not be like a limit, perhaps especially. It'd be like the negation of a limit.

Reply to jgill
And, here, I thought that I was just defending a point. Y'know it kind of reminds me of this story that I once heard about a man with a peculiar manner of speech who lived in a city where everyone spoke perfect Standard English. He suffers from schizophrenia and becomes convinced that everyone there has developed telepathy. Needless to say, he doesn't get on very well and eventually dies in some nameless alley outside of a world renowned theatre. I can't remember the name of it or its author, but I recall reading in an interview that they said that it was about Victorian mentalism. That or to have been inspired by A Brave New World. What's the difference, really?

Quoting thewonder

When you divide by zero, you can say that it is positive infinity.

Why does the positive get priority?

If you do 1/-0.1 you get -10,
1/-0.01 you get -100,
1/-0.001 you get -1000
...
1/-0.0000000001 you get -10000000000
...
1/-0.000000000000000000000000000001 you get -1000000000000000000000000000000
...
clearly getting bigger and bigger negative numbers as the x in 1/x gets closer to 0
...
but then when the x in 1/x actually gets all the way down to 0, suddenly instead of being negative "almost infinity", at that last step it flips sign around to positive infinity? Why?

Quoting thewonder

When you divide by positive or negative infinity, you can say that it is zero

Setting aside the problem that you can only divide by numbers and infinity is definitionally bigger than any number and so not a number... given the above problem with dividing by zero to get infinity, you have the same problem in reverse with dividing by infinity to get zero. If 1/? = 0 and 1/-? = 0, then what's the reverse? 1/0 = ? or -??

Reply to Pfhorrest
I don't know. Perhaps such a mathematical system would only include positive numbers? Like I said, I have yet to hash this all out.

Anyways, I have left this forum again, and, so, will say "so long!"