Zero divided by Zero equals 0 & 1 & ∞

[Dalek Prime]

coming from the most learned man south of the equator.

The competition is weak in my part of the world, Harbal, mostly due to the hot weather and cold beer.

I fear Hobbes will still find fault with it, he won't be able to prevent himself.

Indeed Hobbes is a pedagogue with a style unique to himself and I've no doubt you're quite right.

One thing I've noticed from Hobbes, if you sift through his posts; he'll say he disagrees with you, all the while repeating the essence of what you just said, in his own words.

[Philosophy Explorer]

coming from the most learned man south of the equator.

The competition is weak in my part of the world, Harbal, mostly due to the hot weather and cold beer.

I fear Hobbes will still find fault with it, he won't be able to prevent himself.

Indeed Hobbes is a pedagogue with a style unique to himself and I've no doubt you're quite right.

One thing I've noticed from Hobbes, if you sift through his posts; he'll say he disagrees with you, all the while repeating the essence of what you just said, in his own words.

In the words of Hex, he's a "parrot."

PhilX

[JSS]

As best I can tell, the equation 0/0 has three different answers which means that 1=2=∞. So now what the fnck?

The logic behind math is often forgotten. The division symbol refers to how many times the upper number is going to be divided up.

"24/1" means that the number 24 is to be divided up into a single set that sums to 24, which would be 24.
"24/2" means that the number 24 is to be divided up into two equal sets that sum to 24, each which would be 12.
"24/3" means .... sets that sum to 24, each of which would equal 8.
..and so on.

So following that standard of logic language:
"24/0" means that the number 24 is to be divided up into zero sets, no sets, which must sum up to 24, which means that it is impossible. It would take more than an infinity of zeros to sum to 24, thus the answer would have to be greater than infinity. Without hyperreal math or at least designated cardinalities, no degree of infinite zeros can sum up to 24.

If you take it to the abstract extreme and consider the denominator to be the lowest possible number and the numerator to be the largest possible number (regardless of carnality), then the division requires a number greater than the largest possible number. That is why it is impossible.

So the answer is not 1, nor 2, nor ∞.
The term is an oxymoron, a square circle, an impossibility.

[Philosophy Explorer]

As best I can tell, the equation 0/0 has three different answers which means that 1=2=∞. So now what the fnck?

The logic behind math is often forgotten. The division symbol refers to how many times the upper number is going to be divided up.

"24/1" means that the number 24 is to be divided up into a single set that sums to 24, which would be 24.
"24/2" means that the number 24 is to be divided up into two equal sets that sum to 24, each which would be 12.
"24/3" means .... sets that sum to 24, each of which would equal 8.
..and so on.

So following that standard of logic language:
"24/0" means that the number 24 is to be divided up into zero sets, no sets, which must sum up to 24, which means that it is impossible. It would take more than an infinity of zeros to sum to 24, thus the answer would have to be greater than infinity. Without hyperreal math or at least designated cardinalities, no degree of infinite zeros can sum up to 24.

If you take it to the abstract extreme and consider the denominator to be the lowest possible number and the numerator to be the largest possible number (regardless of carnality), then the division requires a number greater than the largest possible number. That is why it is impossible.

So the answer is not 1, nor 2, nor ∞.
The term is an oxymoron, a square circle, an impossibility.

What's your interpretation of 24/.5?

PhilX

[JSS]

As best I can tell, the equation 0/0 has three different answers which means that 1=2=∞. So now what the fnck?

The logic behind math is often forgotten. The division symbol refers to how many times the upper number is going to be divided up.

"24/1" means that the number 24 is to be divided up into a single set that sums to 24, which would be 24.
"24/2" means that the number 24 is to be divided up into two equal sets that sum to 24, each which would be 12.
"24/3" means .... sets that sum to 24, each of which would equal 8.
..and so on.

So following that standard of logic language:
"24/0" means that the number 24 is to be divided up into zero sets, no sets, which must sum up to 24, which means that it is impossible. It would take more than an infinity of zeros to sum to 24, thus the answer would have to be greater than infinity. Without hyperreal math or at least designated cardinalities, no degree of infinite zeros can sum up to 24.

If you take it to the abstract extreme and consider the denominator to be the lowest possible number and the numerator to be the largest possible number (regardless of carnality), then the division requires a number greater than the largest possible number. That is why it is impossible.

So the answer is not 1, nor 2, nor ∞.
The term is an oxymoron, a square circle, an impossibility.

What's your interpretation of 24/.5?

PhilX

Well, let's see...
"24/2" means that the number 24 is to be divided up into two equal sets that sum to 24, each set would be 12.

"24/0.5" means that the number 24 is to be divided up into half a set that sums to 24, each set would be 48.

[Philosophy Explorer]

What's your interpretation of 24/.25?

PhilX

[Obvious Leo]

As best I can tell, the equation 0/0 has three different answers which means that 1=2=∞. So now what the fnck?

The logic behind math is often forgotten. The division symbol refers to how many times the upper number is going to be divided up.

"24/1" means that the number 24 is to be divided up into a single set that sums to 24, which would be 24.
"24/2" means that the number 24 is to be divided up into two equal sets that sum to 24, each which would be 12.
"24/3" means .... sets that sum to 24, each of which would equal 8.
..and so on.

So following that standard of logic language:
"24/0" means that the number 24 is to be divided up into zero sets, no sets, which must sum up to 24, which means that it is impossible. It would take more than an infinity of zeros to sum to 24, thus the answer would have to be greater than infinity. Without hyperreal math or at least designated cardinalities, no degree of infinite zeros can sum up to 24.

If you take it to the abstract extreme and consider the denominator to be the lowest possible number and the numerator to be the largest possible number (regardless of carnality), then the division requires a number greater than the largest possible number. That is why it is impossible.

So the answer is not 1, nor 2, nor ∞.
The term is an oxymoron, a square circle, an impossibility.

I agree with this more intuitive understanding of the zero, as did the Persians who inherited the zero from the Hindus. They didn't regard zero as a real number at all but just as a convenient symbol for NOTHING and nothing does not exist. Thus to add, subtract, multiply or divide any number by zero was to do NOTHING to the number and therefore such as abstraction did not constitute an equation.

[Philosophy Explorer]

As best I can tell, the equation 0/0 has three different answers which means that 1=2=∞. So now what the fnck?

The logic behind math is often forgotten. The division symbol refers to how many times the upper number is going to be divided up.

"24/1" means that the number 24 is to be divided up into a single set that sums to 24, which would be 24.
"24/2" means that the number 24 is to be divided up into two equal sets that sum to 24, each which would be 12.
"24/3" means .... sets that sum to 24, each of which would equal 8.
..and so on.

So following that standard of logic language:
"24/0" means that the number 24 is to be divided up into zero sets, no sets, which must sum up to 24, which means that it is impossible. It would take more than an infinity of zeros to sum to 24, thus the answer would have to be greater than infinity. Without hyperreal math or at least designated cardinalities, no degree of infinite zeros can sum up to 24.

If you take it to the abstract extreme and consider the denominator to be the lowest possible number and the numerator to be the largest possible number (regardless of carnality), then the division requires a number greater than the largest possible number. That is why it is impossible.

So the answer is not 1, nor 2, nor ∞.
The term is an oxymoron, a square circle, an impossibility.

I agree with this more intuitive understanding of the zero, as did the Persians who inherited the zero from the Hindus. They didn't regard zero as a real number at all but just as a convenient symbol for NOTHING and nothing does not exist. Thus to add, subtract, multiply or divide any number by zero was to do NOTHING to the number and therefore such as abstraction did not constitute an equation.

Here me and Leo differ. I count zero (along with modern mathematicians) as a real number because in addition and multiplication with zero, it leads to another number and it's consistent with the laws of algebra so it makes sense. People get confused when they equate zero to ideas such as distance e.g. and say that it can't exist because there's no such thing as zero distance, but that's irrelevant because it's a matter of interpretation. By not restricting zero to a physical interpretation gives it power to be applied in a number of different mathematical settings which has helped advance mathematics. Also if you follow Leo's reasoning to its logical conclusion based on his premises, then he's denying negative numbers, fractions, imaginary numbers, irrational numbers and other types of numbers. Again there is nothing in logic that supports Leo's narrow interpretation of what a number is (let alone that there still isn't a definition of number).

PhilX

[JSS]

By not restricting zero to a physical interpretation gives it power to be applied in a number of different mathematical settings which has helped advance mathematics.

Do you have an example of that for clarification?

I was thinking in terms of set theory.

[Philosophy Explorer]

By not restricting zero to a physical interpretation gives it power to be applied in a number of different mathematical settings which has helped advance mathematics.

Do you have an example of that for clarification?

I was thinking in terms of set theory.

As far as set theory goes, I don't see where Jaded Sage has referred to set theory in his postings.

But since you're referring to set theory, I can bring up the empty set which is set theory's way of saying zero which isn't referring to anything physical. The numeral zero is used as a placeholder. I sometimes rewrite numbers, e.g.
I would rewrite 7 as 07 which has the same meaning as 7 and lets me keep numbers aligned, in computer work sometimes it's advantageous to start off with zero other than one for some reason (I'm not the expert here on this - I just happen to know it's true - someone like Scott Mayer could explain why this is), in Boolean/binary logic we have 0 and 1, etc.

What do you think?

PhilX

[JSS]

Do you have an example of that for clarification?

I was thinking in terms of set theory.

As far as set theory goes, I don't see where Jaded Sage has referred to set theory in his postings.

But since you're referring to set theory, I can bring up the empty set which is set theory's way of saying zero which isn't referring to anything physical. The numeral zero is used as a placeholder. I sometimes rewrite numbers, e.g.
I would rewrite 7 as 07 which has the same meaning as 7 and lets me keep numbers aligned, in computer work sometimes it's advantageous to start off with zero other than one for some reason (I'm not the expert here on this - I just happen to know it's true - someone like Scott Mayer could explain why this is), in Boolean/binary logic we have 0 and 1, etc.

What do you think?

PhilX

Well, okay. Now I see where you are going.

The two numbers in a division term are not of the same type. The numerator represents a set to be divided. But the denominator represents a count, how many divisions. Numbers can represent different kinds of concepts. You have given an example of a zero being used merely as a symbol to infer the possibility of something in an order, a "place holder". That is yet another kind of concept that numbers can be used for (as symbols). Binary uses the order of 1's and 0's to represent states; "on and off", "true and false", "existent and nonexistent".

Mathematics is a language with which to deal with the logic involved in measurements and quantities. Some try to use it in more mystical ways to imply magical things. Some try to use it to construct complete ontologies, conflating the map with the terrain.

I'm strictly the rational kind of guy.

[Obvious Leo]

I'm strictly the rational kind of guy.

Me too.

Some try to use it to construct complete ontologies, conflating the map with the terrain.

I can never resist an opportunity to fling this logical fallacy into the snake pit of physics but the priesthood seems unwilling to acknowledge its error.

[JSS]

Some try to use it to construct complete ontologies, conflating the map with the terrain.

I can never resist an opportunity to fling this logical fallacy into the snake pit of physics but the priesthood seems unwilling to acknowledge its error.

The "priesthood" knows that they get their power through mental mysticism. They don't like being constrained by reality.

[Obvious Leo]

The "priesthood" knows that they get their power through mental mysticism. They don't like being constrained by reality.

Refusing to allow the facts to fuck up a good story is a common human foible but possibly not a desirable characteristic in a man of science. I reckon a distinction must always be maintained between how zero can be used in a purely abstract mathematical exercise and the conclusions which can then be drawn from such an exercise about the nature of physical reality. This is the same point I was making in our other conversation about infinity. Leibniz made the same point in his argument with Newton about the ontological status of the calculus. Gottfried was of the view that the calculus was a useful tool to describe the way a physical system TENDS but it could no be used to make truth statements about a system's actual physical state. Unfortunately Newton won this argument which he should have lost and bequeathed his victory to the science of physics which he founded. Thus the problem with physics is not just a metaphysical one but also a meta-mathematical one because Newton's tools are actually the cause of this conflation between the map and the territory.

Interestingly Albert Einstein eventually suspected exactly this and revealed his suspicions to John Kemeny not long before he died. Somewhat morosely he conceded that he might have wasted the last forty years of his life by trying to unify the models of physics with the wrong mathematical equipment. He should have been listening to Henri Poincare before he ever allowed that moron Minkowski to lay waste to his remarkable intuition. Poincare was the true father of modern relativity theory, and he rejected Minkowski's model immediately and emphatically, but the geo-political realities of the era were such that no German would ever allow himself to be corrected by a Frenchman. This was Einstein's first mistake but it laid the groundwork for a few more.

[JSS]

I reckon a distinction must always be maintained between how zero can be used in a purely abstract mathematical exercise and the conclusions which can then be drawn from such an exercise about the nature of physical reality.

Science dropped the early requirements to solidly define exactly what one means with the words and symbols one uses. That, to me, is the cause of the current very imaginative conflation of utter nonsense with actual falsifiable science. I suspect it to have been intentional for socio-political stratagems.

This is the same point I was making in our other conversation about infinity. Leibniz made the same point in his argument with Newton about the ontological status of the calculus. Gottfried was of the view that the calculus was a useful tool to describe the way a physical system TENDS but it could no be used to make truth statements about a system's actual physical state.

They had to have been referring to something specific. Calculus yields perfectly correct answers for demonstratively physical shapes, forms, timings, pressures, and so on. As far as I know, calculus has never been found to yield an incorrect answer. And the reasoning behind it is pretty straightforward and logical.

Do you have an example of exactly what kind of situation they were thinking of wherein calculus would not yield a proper physical model or prediction?

Interestingly Albert Einstein eventually suspected exactly this and revealed his suspicions to John Kemeny not long before he died. Somewhat morosely he conceded that he might have wasted the last forty years of his life by trying to unify the models of physics with the wrong mathematical equipment. He should have been listening to Henri Poincare before he ever allowed that moron Minkowski to lay waste to his remarkable intuition. Poincare was the true father of modern relativity theory, and he rejected Minkowski's model immediately and emphatically, but the geo-political realities of the era were such that no German would ever allow himself to be corrected by a Frenchman. This was Einstein's first mistake but it laid the groundwork for a few more.

I'm pretty sure being German wasn't the issue (Minkowski obviously had a screw or two loose). And I am not familiar with arguments that Einstein had against calculus...?