Can God divide by zero?

[JDaniel]

It is hard to “grab” infinity, so I will give a different example. Suppose there is a chocolate manufacturer, and wants to advertize its product. Into every box of chocolate they place a coupon. If you collect 10 coupons, you will get a box of chocolate free. Suppose each box costs 1 dollar. The question is: “how much is one box of chocolate worth?”. I will use two methods to show the result.

1. A box of chocolate is worth a little more than the 1 dollar, since it also contains the coupon. (The coupon is worth 0.1 dollar. Remember, 10 coupons earn a new box.) But, the coupon is worth 1/10th of a box of chocolate. To that 1/10th of a box belongs 1/100th of the coupon. The 1/100th of the coupon is worth 1/1000th of box, etc… ad infinitum. So one box is really worth 1 + 1/10 + 1/100 + 1/1000 + … = 1.11111… dollars.
2. Now, suppose you already accumulated 9 coupons (and spent 9 bucks). You go to the store, grab a box, extract the 10th coupon, go to the cashier and present the 10 coupons as payment. So for 9 dollars you got 10 chocolates, therefore each box is worth precisely 10/9 dollars.

So, 1.1111111111… = 10/9. Not “approximately”, exactly, precisely. And there you have your actual infinity.

Spock:

Would you mind doing me a big favor? Please write that number out for me, all the way to the final decimal place. If takes you a while, that’s OK. I don’t mind waiting.

You see, the problem is: I need to lay my eyes on it in order to believe it. Otherwise, you could be blowing smoke.

In the mean time, maybe we could go to the store where they sell that chocolate and buy a box, so that we can get another infinity going. Are you still in Europe?

God bless,
jd

 

[Spock]

Spock:

Would you mind doing me a big favor? Please write that number out for me, all the way to the final decimal place. If takes you a while, that’s OK. I don’t mind waiting.

You see, the problem is: I need to lay my eyes on it in order to believe it. Otherwise, you could be blowing smoke.

In the mean time, maybe we could go to the store where they sell that chocolate and buy a box, so that we can get another infinity going. Are you still in Europe?

God bless,
jd

I wonder if you are serious. I assume you are, so I will answer in detail. There it is: “10/9”. All the decimal places are there. Very simple mathematics. But I will ask you back: If you think that they are not equal, exactly and precisely, what is the difference?

Way back, when the Greeks contemplated a similar problem they posited a paradox about Achilles and the turtle. They said that in a race between Achilles and the turtle, if Achilles gives an advantage to the turtle, then he will never catch it. Their reasoning was: During the time when Achilles reaches the point where the turtle is, the turtle moves forward. Then Achilles must reach that point, but then the turle will move forward again, etc… so their conclusion was: “Logic shows that Achilles can never reach the turtle”. On the other hand obviously Achilles can overtake the turtle. So the poor suckers were baffled.

Zenon posited it differently: he said that an arrow can never reach the wall, since it must cover the distance halfway to the wall. Then it must cover half of the remaining distance. Then the half again… etc. (He posited the problem of “1/2 + 1/4 + 1/8 + …” ). Obviously, the arrow does reach the wall. (1/2 + 1/4 + 1/8 + … = 1 - exactly and precisely)

Their confusion easy to understand - today. They had no idea about convergent and divergent series. They simply thought that if you add up infinitely many numbers, the result will also be infinite. Of course, there is no surprise. Their thought process was encumbered by their lack of knowledge.

Those old guys were pretty smart on their level. Looking back from our perspective today their speculations are very primitive. They were not dumb, just ignorant. So they submitted speculations, because they lacked the sufficient foundation. Their speculations have nothing to offer us. (On the other hand, whe Euclide established his geometry, he was not speculating. When Pythagoras proved his theorem, he did not speculate.) That is why I am smiling when I see that the empty speculations of Aristotele, Plato, Aquinas, etc… are held in such a high esteem by Catholics. Get out of the “stone age”, guys.

 

[JDaniel]

I wonder if you are serious. I assume you are, so I will answer in detail. There it is: “10/9”. All the decimal places are there. Very simple mathematics. But I will ask you back: If you think that they are not equal, exactly and precisely, what is the difference?

Way back, when the Greeks contemplated a similar problem they posited a paradox about Achilles and the turtle. They said that in a race between Achilles and the turtle, if Achilles gives an advantage to the turtle, then he will never catch it. Their reasoning was: During the time when Achilles reaches the point where the turtle is, the turtle moves forward. Then Achilles must reach that point, but then the turle will move forward again, etc… so their conclusion was: “Logic shows that Achilles can never reach the turtle”. On the other hand obviously Achilles can overtake the turtle. So the poor suckers were baffled.

Zenon posited it differently: he said that an arrow can never reach the wall, since it must cover the distance halfway to the wall. Then it must cover half of the remaining distance. Then the half again… etc. (He posited the problem of “1/2 + 1/4 + 1/8 + …” ). Obviously, the arrow does reach the wall. (1/2 + 1/4 + 1/8 + … = 1 - exactly and precisely)

Their confusion easy to understand - today. They had no idea about convergent and divergent series. They simply thought that if you add up infinitely many numbers, the result will also be infinite. Of course, there is no surprise. Their thought process was encumbered by their lack of knowledge.

Those old guys were pretty smart on their level. Looking back from our perspective today their speculations are very primitive. They were not dumb, just ignorant. So they submitted speculations, because they lacked the sufficient foundation. Their speculations have nothing to offer us. (On the other hand, whe Euclide established his geometry, he was not speculating. When Pythagoras proved his theorem, he did not speculate.) That is why I am smiling when I see that the empty speculations of Aristotele, Plato, Aquinas, etc… are held in such a high esteem by Catholics. Get out of the “stone age”, guys.

I would answer like so:

Collect 10 Coupons And You Will Get A Box Of Chocolates Free. If Each Box (Containing 1 Coupon) Costs $1.00 Dollar. Then For $10.00 I’ll Receive 11 Boxes. How Much Did Each Of The 11 Boxes Cost Me?

The Answer Is:
1000 Cents = 90.90909091 Cents (or, to potential infinity, since there can be no final number)
11 Boxes

Fractions seemingly present a counter to this. But, if we take an actual, such as a beaker of water, we can divide it in half. That half can be further divided into halves. And so on, until we arrive at molecular water. Then, the actual water can only be divided into hydrogen and oxygen. This can be extrapolated to everything real, i.e., actual.

Catholics are not speculating in the past, we are properly defining two words: “infinity” and “actual.” (Some of) today’s mathematicians are not. (Some of) today’s mathematicians are equivocating. Infinity is by definition ambiguous. It is not a fixed number. There can be no number Infinity. There can be no quantity Infinity. A series of numbers would be actually infinite if it contained all possible numbers and if, as a result, no new number could be added to the series. Explain how this is wrong. I am not interested in seeing an explanation that employs set theory, which is nothing more than a reification, i.e., an abstraction: it is the arbitrary closing of a group of numbers.

I am familiar with Zeno’s Paradox. Paradoxes can be created by unfortunate equivocations. I will not use the word “actual” in an equivocating manner. I will not use the word “infinity” in an equivocating manner. When the two words are strung together, there must be no equivocation. If “infinity” is used to represent a number where a new number, such as a “1”, or a series of “1’s”, can be added to the series, that is equivocation. Where “actual” is used to represent something that can only be thought, that is equivocation. Why is it that only the Scholastics are honest enough to admit this? (Pre-emptively, I know that many mathematicians that are honest enough to admit it, too.)

God bless,
jd

 

[sidbrown]

A series of numbers would be actually infinite if it contained all possible numbers and if, as a result, no new number could be added to the series. Explain how this is wrong.

It is wrong since the set of even integers is an infinite set.

 

[tafan]

I say not. Mathematical truth can not contradict the higher order of the truth, that is God. God can no more divide by zero than he can lie or sin. This is not because he is not omnipotent, but because he is omnipotent, the hightest order of being (metaphysics) and the highest order of truth (epistimology).

very good.

 

[Spock]

I would answer like so:

Collect 10 Coupons And You Will Get A Box Of Chocolates Free. If Each Box (Containing 1 Coupon) Costs $1.00 Dollar. Then For $10.00 I’ll Receive 11 Boxes. How Much Did Each Of The 11 Boxes Cost Me?

The Answer Is:
1000 Cents = 90.90909091 Cents (or, to potential infinity, since there can be no final number)
11 Boxes

Well, you made an error here. For 10 dollars you get 11 boxes PLUS one more coupon, which is worth 1/10th of a box, which in turn has 1/100th of a coupon… etc.

Fractions seemingly present a counter to this. But, if we take an actual, such as a beaker of water, we can divide it in half. That half can be further divided into halves. And so on, until we arrive at molecular water. Then, the actual water can only be divided into hydrogen and oxygen. This can be extrapolated to everything real, i.e., actual.

Numbers can be divided all the way to infinity, there is no “smallest number”, like a water molecule. You will need to look at Cantor sets. Which is the “first” positive number following zero? (Not first positive integer, but the first positive number?)

I am not interested in seeing an explanation that employs set theory, which is nothing more than a reification, i.e., an abstraction: it is the arbitrary closing of a group of numbers.

Surprise! Numbers are abstractions. People used to have a tremendous problem of conceptualizing negative integers, and the concept of zero. They kept wondering what could a “minus one apple” be? It was incomprehensible to them. They could not imagine a “negative distance”.

By the way, set theory cannot be separated from numbers. The modern axiomatic foundation of mathematics is inseparable from set theory.

 

[JDaniel]

It is wrong since the set of even integers is an infinite set.

First of all, even in its exclusionary nature, the so-called set of even numbers is merely a series of words depicting real numbers and as such they, too, can be potentially infinite.

But, aside from that, when you reach that final number, of the set of even numbers, are you telling me that nothing more that can be added? Can I not add another “2”? Can I not add a small series of “2’s”?

Is there a final number of the set of even numbers? Does it have a name, i.e., a sound that indicates that it is a natural number?

God bless,
jd

 

[JDaniel]

Well, you made an error here. For 10 dollars you get 11 boxes PLUS one more coupon, which is worth 1/10th of a box, which in turn has 1/100th of a coupon… etc.

Yep. You’re right.

Numbers can be divided all the way to infinity,

If that is so, then we should have no trouble determining what number is infinity?

. . .there is no “smallest number”, like a water molecule. You will need to look at Cantor sets. Which is the “first” positive number following zero? (Not first positive integer, but the first positive number?)

Is there not a Peano axiom that says, that for every natural number, there is exactly one natural number that is its successor? And, zero is the successor of . . .?

Surprise! Numbers are abstractions.

Oops! I must have missed that.

People used to have a tremendous problem of conceptualizing negative integers, and the concept of zero. They kept wondering what could a “minus one apple” be? It was incomprehensible to them. They could not imagine a “negative distance”

.

When they were first introduced to me, as a 4th or 5th grader, I know I did.

By the way, set theory cannot be separated from numbers. The modern axiomatic foundation of mathematics is inseparable from set theory.

While this is true, one cannot merely place brackets around a set and then say, “There, that’s a real, actual list of all the numbers! Well, I know there not all there, but, you have to imagine that those dots are them. Oh, and they correspond, one to one, to all of those grains of sand on the beach. Whew! There must be an infinity of them out there.”

Are you still in Europe?

God bless,
jd

 

[Vico]

Anyone can divide by zero. The problem is understanding the answer. It is some sort of infinity. But which sort? There is actually infinite orders of infinity.

Presumably God does understand all orders of infinity.

Let a = b

a^2 = ab

a^2 - b^2 = ab - b^2

Factorise:

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

Cancel the common factor, (a-b) and we have:

a+b = b

Since a = b this gives:

2b = b

Cancel common factor, b.

2 = 1

QED

If you cancel the common factor, it is division, which cannot be done by zero, so a <> b.

 

[sidbrown]

Is there a final number of the set of even numbers?

That is the difference between a finite set of numbers and an infinite set of numbers.

 

[JDaniel]

That is the difference between a finite set of numbers and an infinite set of numbers.

So, you would say, that the finite set has a natural end number and the infinite set has an ambiguity?

God bless,
jd

 

[sidbrown]

So, you would say, that the finite set has a natural end number and the infinite set has an ambiguity?

God bless,
jd

I would not agree with the misuse of the term ambiguity in this context.

 

[JDaniel]

I would not agree with the misuse of the term ambiguity in this context.

Why would that be a misuse?

 

[sidbrown]

Why would that be a misuse?

Because there is no ambiguity involved. There is nothing unclear, uncertain, or equivocal about the definition of a set of infinite numbers, which i have already given above.

 

[JDaniel]

Because there is no ambiguity involved. There is nothing unclear, uncertain, or equivocal about the definition of a set of infinite numbers, which i have already given above.

Then tell what that number is - the end number in the set. Even if I can’t pronounce it, I’ll give it a try.

God bless,
jd

 

[Spock]

If that is so, then we should have no trouble determining what number is infinity?

Mathematicians have no trouble. The first infinity is denoted by aleph-zero. And there are infinitely many infinities out there. Look it up here: en.wikipedia.org/wiki/Aleph_number

Is there not a Peano axiom that says, that for every natural number, there is exactly one natural number that is its successor? And, zero is the successor of . . .?

I explictly talked about the positive numbers, not just the positive integers. Take the numbers between zero and one, without the two end points. There is no “first” or “last” number in that interval.

When they were first introduced to me, as a 4th or 5th grader, I know I did.

Naturally. Probably everyone has difficulties for a while.

While this is true, one cannot merely place brackets around a set and then say, "There, that’s a real, actual list of all the numbers! Well, I know there not all there, but, you have to imagine that those dots are them.

What is your problem with it? A new notation to describe something new happens all the time. When you multiply any real number with itself, the result will always be a positive number. Yet, the question: “which number is what yields minus one, when multiplied by itself?” is valid, and it can be answered. This number is usually denoted by “i”. Is it a “valid” number? You bet. Is it a “real” number. No, since the word “real” in mathematics is reserved for the numbers residing on the number line". No ambiguity there, just an unfortunate selection of terminology.

Are you still in Europe?

Yes.

 

[JDaniel]

Mathematicians have no trouble. The first infinity is denoted by aleph-zero. And there are infinitely many infinities out there. Look it up here: en.wikipedia.org/wiki/Aleph_number

An infinity of infinities! It’s too bad that mathematicians stopped using the real meaning of the word. But, then, they would not have had as much fun.

Mathematics: a number greater than any assignable quantity or countable number (symbol ∞). - Oxford Dictionary Online

“The aleph numbers differ from the infinity (∞) commonly found in algebra and calculus. Alephs measure the sizes of sets; infinity, on the other hand, is commonly defined as an extreme limit of the real number line (applied to a function or sequence that “diverges to infinity” or “increases without bound”), or an extreme point of the extended real number line.” - Wikipedia

These definitions are extremely divergent. It’s almost as though mathematicians purposely ambiguated the definition. They could have called it some other name, but, instead hijacked an existing concept that was non-ambiguously ambiguous and that dated back to at least the Greeks, like Anaxagoras. Today, it is clearly the cause of much confusion.

I explictly talked about the positive numbers, not just the positive integers. Take the numbers between zero and one, without the two end points. There is no “first” or “last” number in that interval.

Because they are fractions, and can continue to be divided ad infinitum, to that non-end-point reification, out there, that we call infinity!

What is your problem with it? A new notation to describe something new happens all the time. When you multiply any real number with itself, the result will always be a positive number. Yet, the question: “which number is what yields minus one, when multiplied by itself?” is valid, and it can be answered. This number is usually denoted by “i”. Is it a “valid” number? You bet. Is it a “real” number. No, since the word “real” in mathematics is reserved for the numbers residing on the number line". No ambiguity there, just an unfortunate selection of terminology.

That described my problem with it. And, “valid” has to do with “acceptability,” or, “reasonability.” Quite different from “reality”.

Vacation, or, a special trip? What part or, parts, of Europe?

Stay safe and God bless,
jd

 

[Spock]

An infinity of infinities! It’s too bad that mathematicians stopped using the real meaning of the word. But, then, they would not have had as much fun.

Mathematics: a number greater than any assignable quantity or countable number (symbol ∞). - Oxford Dictionary Online

“The aleph numbers differ from the infinity (∞) commonly found in algebra and calculus. Alephs measure the sizes of sets; infinity, on the other hand, is commonly defined as an extreme limit of the real number line (applied to a function or sequence that “diverges to infinity” or “increases without bound”), or an extreme point of the extended real number line.” - Wikipedia

These definitions are extremely divergent. It’s almost as though mathematicians purposely ambiguated the definition. They could have called it some other name, but, instead hijacked an existing concept that was non-ambiguously ambiguous and that dated back to at least the Greeks, like Anaxagoras. Today, it is clearly the cause of much confusion.

Nope, they are not. They approach the same concept in a different fashion.

Because they are fractions, and can continue to be divided ad infinitum, to that non-end-point reification, out there, that we call infinity!

What is your point? Look at the Cantor-set (en.wikipedia.org/wiki/Cantor_set) which has a “size” of zero, and which has infinitely many elements.

That described my problem with it. And, “valid” has to do with “acceptability,” or, “reasonability.” Quite different from “reality”.

If you wish to talk about any specific subject you cannot avoid its specific terminology. Sometimes the chosen terminology is unfortunate. It happens in mathematics, too. To call certain numbers “rational” and others “irrational” to call certain numbers “real” and others “imaginary” were particularly bad choices, causing a lot of confusion. But mathematics is nothing but a mind-game, which can be applied to actual reality very well.

Vacation, or, a special trip? What part or, parts, of Europe?

Retirement + trips + vacations + fun + family + books + games + … ad infinitum.

 

[stringbeanduck]

God can (of His own will) bind Himself to the laws we are bound to, but He is not bound laws we are bound to. For example, Jesus subjected Himself to a human body, but God didn’t have to do that.

All the physical laws that we know of now, and will continue to discover came from God. Although we can not imagine a reality where a number can be divided by zero, God can. However, this reality was the one He gave to us, thus division by zero is not possible, by anyone for these laws given.

 

[sidbrown]

Then tell what that number is - the end number in the set. Even if I can’t pronounce it, I’ll give it a try.

God bless,
jd

Pronunciation is irrelevant to the discussion.
For the infinite set of integers: { …,-3,-2,-1,0,1,2,3,…} there is no first or last number. If you want an example of a set of infinite numbers, with a first and last number, you can consider the closed interval [0,1], which is the set of all x with x between 0 and 1, where x can take on the values of 0 or 1. If you restrict x to be a rational number, then this will be a countable, infinite set.