Mathematical Logic

divide by infinity is 0,..... isn't '∞' a concept and not a number

In making mathematical operations to something, the book says and it is taught on universities you can not add ham and egg all together, in breakfast perhaps you can.

Well, in this case "∞" is an enormous number. Do you agree?

No

can it be plotted out?

Yes.

Well this guy had created something from infinity (∞) and it was so brilliantly psychedelic.

Yes, but there's no "s". It's L'Hopital, not L'Hospital.

Here is a good simple link dealing with infinity:

http://www.vitutor.com/calculus/limits/properties_infinity.html

If that equation was plotted using the y intercept formula of y=mx+b all the points would be on 0.

No offense implied...

http://www.amazon.com/Calculus-Dummies-Mark-Ryan/dp/1118791290/ref=sr_1_1?s=books&ie=UTF8&qid=1439398017&sr=1-1&keywords=calculus+for+dummies

Or maybe:

No offense here either.

Do you know that there is now a "String Theory for Dummies" book?

I just saw it on Amazon! http://www.amazon.com/String-Theory-Dummies-Andrew-Zimmerman/dp/047046724X/ref=pd_bxgy_14_text_y#reader_047046724X

What next? "Rebuilding your Porsche 918 for Dummies"

At the very least the mythical "Porsche 918 for Dummies" book will produce verifiable tests one can actually perform. "String theory for dummies" will require three black holes and a white hole to be oriented with a relativistic tachyon beam to trisect space in a tesseract configuration to test one of many hypotheses.

Haha! I'm not sure about that. You know that nearly all (I'm being conservative) of the documents on German car parts, build and software have errors. The original design calls for a 286-9845502, but during production we found that these parts come loose by the time the car gets to the port, so they changed to 486-0003743. Then they found out that those parts start to rust, so they had the manufacturer add paint, thus a new part number 496-0000122. Right before production for that year was completed, they ran out of parts, so they went to another manufacturer and put in part 2-098-453002. Mercedes is also notorious for doing this, as well as BMW, Audi and VW (except VW gives the same part number for two different parts - they must've learned this trick from GM).

I can see it now! "Porsche 918 Repairs for Dummies" - That round thing with the cross in the middle is called a Phillips Head Screw. You remove this screw by putting a Phillips Head Screwdriver into the cross and turning it counter clockwise. There are 28 screws holding on the lower engine cover, except if you have a car with a s/n higher than 105, then there are 33 screws or if you have a s/n higher than 420 you must use a Torx screwdriver to remove the 39 Torx screws. On s/n greater than 463, be careful not to chip the paint on the screws, except for s/n greater than 498, where the screws are not longer painted. Completely remove the cover and you now have access to the oil filter and oil drain plug on the oil sump tank ...

∞ is not a number! It means a value without an upper bound. None of the statements that you made are mathematically valid. For example your first statement, "N/∞=0" is meaningless. What is valid would be " The limit of of A/X, as X increases without bound, approaches 0. This implies that any A/X (where neither A nor X= 0) can not = 0. As for your second statement: Any number, regardless how large, multiplied by 0 = 0 .

This should all be made crystal clear in your first semester of Calculus.

Who says so, but do you agree? What insight can you relate this one to a reversal? Reversal pass by or touch zero.

Who says so? Mathematicians. Mathematicians have agreed on basic definitions and assumptions and from these have built a powerful tool which has proven useful to Humankind.

Infinity is not a number. Infinity is not a member of the set of Integers or the set of Real Numbers or the set of Natural Numbers or the Set of Imaginary Numbers or any other set whose members can be operated on by addition or other operators. This is by definition.

Ν⁄∞=0 may look like a Mathematical sentence, but it is not a Mathematical sentence. It is Mathematical nonsense.

In closing, I would like to say "Cornflake whenever up to fishing was."

And does it make you believe, what you are told? Well, good for you, you set your boundary already and became fixated on that. I am not.

"Your 'reality,' Sir, is nothing but lies and balderdash, and I am happy to say I have no grasp of it whatsoever." -Baron Munchhausen

You say "As for your second statement: Any number, regardless how large, multiplied by 0 = 0 ."

Not if the small number approaches 0 faster than the big one approaches ∞.

Try it with 1/x²*x as x → 0. That → (∞)(0). But it = 1/x so → ∞ as x → 0.

Any number, regardless how large, multiplied by 0 is 0. This is a definition.

In your example, you never multiply by 0, so you do not contradict the definition.

As x approaches 0, it will never reach 0. That is what x → 0 means.

Sometimes it is important to know whether x is approaching from the right (getting smaller) or from the left (getting bigger), but it doesn't make any difference in this case. x never gets to 0.

I'm not aware of that being an accepted definition in math(s), or how it would be useful if it is, but you might be right.

In Limit (1/x²*x) I do multiply by 0 (or something infinitesimally close). It's just that 1/x² approaches ∞ more quickly. So Limit (1/x²*x) = Limit (1/x) → ∞ as x → 0, although it "equals" ∞*0.

Several posters have mentioned L'hospital's rule. But that is only used when the expression is simplified as far as possible but still leaves an indeterminate form, 0/0 or ∞/∞. E.g. to find Limit (sin(x)/x) as x → 0. It wouldn't be used for Limit (x²/x) as x → 0 as that clearly = Limit (x) = 0.

The Limit can equal a number, but x will never equal the number it is approaching. This is also by definition; x approaches a number, not x eventually reaches a number.

Since division by zero is undefined (not forbidden, undefined. If it doesn't exist, there is no need to forbid it) expressions like y=(1/x) will not exist at x=0. But, the limit of (1/x) as x →∞ will equal 0. The limit will equal 0, but 1/x will never equal 0. There is a distinction.

Is the keeping division by 0 undefined useful? Yes. It eliminates paradoxes.

Massive amounts of mathematical thought are spent on defining what happens in the neighborhood of a number (and neighborhood is the actual term used) and not at the number itself. The first taste of that most students get is in calculus when they learn about limits. Another area where people get a taste of that idea is in statistics when they learn about confidence intervals.

Numbers have more interesting lives than people realize.

That's the point I'm making. As you have rightly pointed out, in Kulas's ∞*0 the ∞ and 0 cannot be treated as actual numbers, but as limits. So the fact that actual 0*anything = 0 is irrelevant. I'm just saying, as in #30, that in Kulas's terms ∞*0 is not necessarily 0.

To take some (more) examples

1. Limit tan(x)*cos(x) as x → pi/2. At first glance that looks like ∞*0 and Kulas might think it's a problem. But of course tan = sin/cos so it = sin(x) = 1 when x = pi/2.

2. Limit tan(x)*(sin(x) - 1) as x → pi/2. That also looks like ∞*0. Writing it as (sin(x) - 1)/cot(x) and using l'Hospital, it = -cos(x)*sin²(x) which = 0 when x = pi/2.

3. Limit tan²(x)*cos(x) as x → pi/2. Also ∞*0. But it = sin²(x)/cos(x) which → +/-∞ as x → pi/2, depending on the direction of approach.

Good examples. Cosine is defined for all values of x. Tangent is not defined for all values of x. But they are still immensely useful, and the limits are well defined.

OK thanks

Plotted 4 dimensionally....

Some says prime numbers can hopefully solve this one.

What is that image? Smoke from Kulas' crack pipe?

I wish Greg, a crack pot could make the world of peace, but nope its an iteration.

Lorentz Attractor - its a beautiful butterfly of Chaos

Although I lust after one, I can't afford to own an Infinity.

To me this is much like the square root of -1 which is used extensively in designing generators, motors, and other electrical devices.

Application of the theory is quite successful however, thoroughly grasping the concept is difficult at times.

Any integer/quantity multiplied by 0 = 0

The higher in value the divisor of any quantity/integer gets as it approaches infinity, the smaller the resultant becomes and approaches the value of "0".

But what would it be like (∞) (0)= be?

L'Hospital's rule applies, again. It all depends on how one reached this indeterminate multiplication.

Never argue with a fool.

Bystanders may not be able to tell the difference.

Easy there friend, a little step a little time, would have a mile displacement later on, sometimes a quantum leap, if get lucky.

Based on the current laws of mathematics, it would still be: 0 - nada - zilch - goose egg

No matter how many zeros are accumulated regardless of the method used, the final quantity value is "zero".

However; You could assign a defined value to the quantity of zeroes. In your case there would be an abstract quantity of "infinity" zeroes.

(∞) (0) is undefined in Mathematics.

However, as RedFred points out, smart people like L'Hôpital have figured out ways to define conditions under which a question which looks very similar to this can be asked. But your exact question can not be asked. It does not make sense.

"To me this is much like the square root of -1 which is used extensively in designing generators, motors, and other electrical devices."

However, the mathematical constant i, (or j, if you majored in Electrical Engineering and already were using i to mean electrical current) is useful because the 'imaginary number' line is at right angles to the 'real number' line, so when you are working with something that changes position AND phase over time, you can describe the signal using complex numbers.

Yes, exactly.

I am very familiar with the j operator and how it is used to calculate magnetic flux density however I do not know where in the Engineering field the (infinity x 0 ) would be used for defining a variable or other quantity.

This is not exactly your requested math of ∞*0=? but here's something similar.

What is the time constant for an ideal constant current source charging up an ideal capacitor?

"We have BOOM in t minus 5rc time constants. 5... 4... 3... 2...

Nowhere in Engineering, unless it's some way to describe the Irresistible Force / Immovable Object paradox⁽¹⁾, but it might be found in a 'summary report' of a process,if the proper 'pre-checks' are not done prior to calculation:

(G/T)*P

Where G = Good product count, T = Total product count, and P = Percentage Multiplier.

The flaw would that G was not cleared to zero when T was, The program does not do a division by zero check, and P was defined as 000 instead of 100 due to a typo..

I've never seen a formula like that, whenever I need to do division in a program or job file, I always put in a zero check ("If T = 0 then 0 , else G/T")after determining what a zero denominator would mean. (In that example, T = Good + Bad, so the actual formula is G/(G+B), and if there is a total count of zero, there is no Good% or Bad%, so I show them as 0% so the display makes sense, (and any automated warnings from a too-high Bad% don't go off.)

Notes:

1. The short answer to that paradox is 'they pass through each other harmesly.' The long answer takes some time:
1. An Irresistible Force is one whose direction and velocity cannot be changed or altered in any way, therefore it cannot interact with normal mater or energy.
2. Due to Relativity, an Immovable Object is no different from an Irresistible Force, it's direction and velocity are fixed and immutable. It just happens to share the same inertial frame of reference as the Observer.
3. Two 'non-interacting' events that meet will, as it says on the tin, not interact with each other or the rest of the universe in general, and would both leave with their original direction and velocity unchanged.
   

I think this falls in the category of: "Can God create a rock that He cannot lift?".

Use the internet.

Mathway | Math Problem Solver

It depends on how ∞ and 0 are approached.

Bearing in mind gringogreg in #7, if it's 1/x²*x as x → 0, that → (∞)(0). But it = 1/x so → ∞ as x → 0.

If it's 1/x*x², it also → (∞)(0) as x → 0. But it = x so → 0 as x → 0.

Or anything in between by the right choice of inputs.

The easiest way to look at this is to consider what happens when you divide a number into a larger and larger number? It gets smaller and smaller, but does it every get to 0?

Ask yourself what infinity is? Is it a number? 0 is a number, right. How about 2.78443? Yes, it's a number. What about 2.78443/0? Is it a number? This will give you the answer you're looking for.

Hmm, interesting that's an untapped realm - a nobel prize.. A week or two months submersion might have an insights on the topic. -

I'm sorry that you don't understand. I thought I would dummy it down for you, because you keep fighting with others on this site.

And if I could win a Nobel Prize, it sure wouldn't be for a "Math for Dummies" entry, now would it.

Its like this, N/∞ = 0 (True/valid or not?) if so then ∞*0 = N, --> this is true, given there is quantifiable infinity and zero.

Only N are quantified, but would you agree that 0 & ∞ does not exist? Then, N does not exist also, since in is a product of both. We solve in general cases variables, any numbers can represented by it.

Some say ∞ and zero can not exist, why not? General concepts of mathematics and physics tells you they exist.

The universe is built that way - bounded by the infinite and nothingness. --A mere pluck of a string, a wave from nothingness and infinite.

Your first equation is wrong. This is where the problem begins. You could write N/x approaches 0 as x approaches infinity. That is correct. Infinity is not a number, where 0 and N are.

Here's a very simple explanation. I really do hope it helps you make sense of it. Just don't fight it. Please.

https://www.mathsisfun.com/numbers/infinity.html

GA!

Well, may be almost all of you haven't seen the angles I am seeing myself. I can not blame you for that, neither mad if you can't agree. "life is like riding a bicycle, to keep in balance we must keep moving"

From your posts in this thread so far, I'm not sure I *WANT* to see the angles you're seeing. They seem so removed from geometry or algebra, that gazing upon them can only lead to madness, like finding a square circle, or a five-sided triangle, or a mathematical set of all numbers NOT in the aforementioned set.

What is next, proving mathematically that 1 = 2? (People try that a lot, but the mathematical trickery involves 'hiding' a division by zero, so if you look at the proof step by step, and plug the numbers into the variables to check the equations, you see where it fails completely.)

You are missing the point of L'Hopital's rule. N/∞ and ∞*0 are not defined by these single arithmetic operations. From personal experience N/∞ is usually equal to zero and ∞*0 is often equal to one. Without the context of how one arrives at these ratios one cannot tell if they equal zero, another number or they still cannot be determined.

Think of this as a mathematical version of an undefined pronoun in a single sentence.

They were exactly what he was hoping for.

From that single sentence one cannot tell who he is, what were his hopes, who they are or even if they are a known group of people. One must read the rest of the paragraph this sentence came from to see if any of these can be defined.

Redfred, Your analogy is right on! I like the outside the box thinking! GA to you!

From The Encyclopedia of Mathematics, via Springer Publishing and in cooperation with the European Mathematical Society:

"The following rules for the mathematical operations are defined for the improper element :

if is finite;

has no meaning;

if ;

has no meaning.

Inequalities involving are not considered; the question as to whether is larger or smaller than a finite number is meaningless."

Was this a law? A principle? An axiom? A theory? if it's not a law, then pretty neat that could be dismissed or refuted anytime when there exist a sound principle or proof.

Now, do you all believe what you are told and taught about? Have you save some discretion for yourself? I don't.

These are definitions, plain and simple. Without definitions, there are no sound principles or proofs. There are no laws or axioms without definitions.

Unlike colloquial human language, mathematics attempts to define its terms precisely so that a mathematician in any part of the world can speak clearly to a mathematician in any other part of the world. No, it's more fundamental than that. Mathematics attempts to precisely define its terms so that one mathematician can speak clearly to the mathematician sitting across the table from him. The definitions I have provided are the definitions that mathematicians use. I am not interested in any others as any other definitions are not useful to a mathematician.

And why have mathematicians chosen these to be the definitions? Because the others have been disproven. They have been proven not useful. They have been proven useless.

However, it you or anyone else were able to demonstrate any counter-example (it only takes one) to disprove the mountains of work already done on these definitions, the world of mathematics will award you the Fields Medal and put your name in the pantheon with Newton, Gauss, Euler, Euclid, et al.

Perhaps there's a little secret about Math that you haven't heard of yet:

It is impossible to 'prove' ANY equation using Formal Logic.

http://www.basicincome.com/bp/logic.htm

This week, a newly elected (less than one year in office) Councilperson tried to get us to approve her letter to the County. A motion was made to take a vote and all of us were given time to explain why we were for or against sending the letter. The responses were in no ways attacking and a lot of good advice was given to her. As you can guess, her letter was voted down 8 to 1 (she voted yes).

That evening, she spoke to a "radical" person in our community who wrote an op ed piece on the vote for the local paper. Amazingly, his piece claimed payoffs and corruption, hence the 8-1 no vote. I don't think he concocted this crazy idea himself, so my guess is that she fed him the idea.

Think about this for a second;

1. She writes a letter that is not correctly written and will not be approved.

2. She receives advice on how to write letters so they can be approved.

3. She refuses to see that her letter is flawed.

4. She creates a story to justify why we won't accept her "perfect" letter.

The message to Kulas is to not be like our Councilperson. You have some very intelligent people here who are trying to help you understand your flawed thinking, yet you continue to make your stand. By all means, I am not as smart as many of the people here and you may be smarter than me, I don't know, but your failure to realize that you made a mistake is very disturbing. You really need to think about it.