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4,188✭So different from this hell I'm living

So different now, from what it seemed

Now life has killed the dream I dreamed

0✭✭✭✭✭6,475Member, Friendly, Cool, Conversationalist ✭✭✭✭✭✭But

1/0≠∞

Sure, it's a number... but a weird one.

Packs: (CC ~ MC ~ BoI ~ DNF)6,436Moderator, Friendly, Helpful, Flagger Modlim

_{(x→∞)}[1/x]=04,188✭So different from this hell I'm living

So different now, from what it seemed

Now life has killed the dream I dreamed

1,692Member ✭✭✭needsme to) and it follows almost all rules of mathematics except for division (which you can actually account for if you think about infinity too)."After all, to the well-organized mind, death is but the next great adventure." -A. Dumbledore

"If you want to know what a man's like, take a good look at how he treats his inferiors, not his equals." -S. Black

“Confidence is ignorance. If you're feeling cocky, it's because there's something you don't know.” -Foaly the Centaur

3,253Member, Internet Detective, Friendly, Idle Game Master, Conversationalist ✭✭✭✭✭4,188✭So different from this hell I'm living

So different now, from what it seemed

Now life has killed the dream I dreamed

5,558Moderator, Friendly, Helpful, Flagger, Conversationalist Mod(proof language is hard to type outside of math programs, so I'm cheating)

1/∞=0 && 2*0=0: therefore=>

2*1/∞=0=1/∞: (simple substitution of equivalent terms)

2*1/∞=1/∞: (now to multiply each side by infinity)

2*1/∞*∞=1/∞*∞: (cancel out like terms) =>

2=1;

Math stops working, because once I prove 1=2, I can use that to prove that (2-1)=(1-1)=>1=0=2. Continuing on in this vein, I can prove that ANY NUMBER=ANY OTHER NUMBER.

But zero is a number. It is a special number. It is

~~neither odd, nor even;~~neither positive, nor negative. Even though it is equal to an integer squared, it isn't a perfect square (a trait that it shares with 1). It isn't prime. It is a placeholder digit, but only when used as a digit (ex. 101 means 1 group of a hundred, placeholder/no groups of ten, and 1 group of one).∞ isn't actually a number, though. It is a placeholder that means "Really gigantic number so large that when you add 1 to it, it is so close to itself that there is no appreciable difference." This is absolutely correct! The only time that you can "divide by zero" is when you are playing around with limits. (Integrals and Derivatives are limits, just special kinds).

Playing with math is FUN!

"10 variants of "I'm a platypus in a human body and only basic sexualities? Meh…" ~Shylight

"You might have me confused for someone who is clever and not lazy." ~Tellurium

"Glorious whatnow? I usually use my brain for tasks like "What should I eat now?" or "Cool, that thing is purple, where can I get that?"" ~DasBloody | "I let the dragon eat the forum" ~Idler | "and don't quote this" ~pinkydash

"You can find my IQ on the part of the bell-curve where the y-axis value approaches zero."

6,475Member, Friendly, Cool, Conversationalist ✭✭✭✭✭✭If you are still doubting...

Packs: (CC ~ MC ~ BoI ~ DNF)5,558Moderator, Friendly, Helpful, Flagger, Conversationalist ModStarting at 1:34, you can have a number that is infinitely close to 1 but still less than 1 (but it isn't .999... or any real number, but infinity isn't a real number either). Likewise, you can have a number that is infinitely close to 0, but still greater than 0. That is what you get when you divide any number by infinity. It gets really fancy when you start getting into indeterminate forms like 0/0, 0

^{0}, 1^{∞}, 0*∞, ∞/∞, or my favorite, ∞-∞."10 variants of "I'm a platypus in a human body and only basic sexualities? Meh…" ~Shylight

"You might have me confused for someone who is clever and not lazy." ~Tellurium

"Glorious whatnow? I usually use my brain for tasks like "What should I eat now?" or "Cool, that thing is purple, where can I get that?"" ~DasBloody | "I let the dragon eat the forum" ~Idler | "and don't quote this" ~pinkydash

"You can find my IQ on the part of the bell-curve where the y-axis value approaches zero."

2,745Member, Friendly, Conversationalist ✭✭✭Actually zero is even, when divided by 2 it has no remainder.

Boots, Brogues, Cleats, Clogs, Flip-flops, Flippers, Galoshes, Getas, Loafers, Oxfords, Mukluks, Moccasins, Pumps, Sandals, Skates, Shoes, Slippers, Sneakers, Socks, Slingbacks, Stilettos, Rollerblades, Tennies, Waders, Wellingtons5,558Moderator, Friendly, Helpful, Flagger, Conversationalist Mod1/∞=0=1/∞:

1/∞=1/∞: (cross-multiply)

∞=∞;

Let me put it another way:

Let x=∞: If I use a variable, I can do algebra with it.

1/x=0 && 2*0=0: therefore=>

2*1/x=0=1/x:

2*1/x=1/x:

2*1/x*x=1/x*x: =>

2=1;

The only way that this doesn't work is if x≠x which would mean that 1/x≠1/x => 1/x≠0. Luckily, ∞≠∞, because ∞ isn't a real number; it is a placeholder for super big number. You are right on this one. I should have looked up the definition of parity before relying on something I learned in math class 8 years ago.

EDIT:

tags don't work.^{}"10 variants of "I'm a platypus in a human body and only basic sexualities? Meh…" ~Shylight

"You might have me confused for someone who is clever and not lazy." ~Tellurium

"Glorious whatnow? I usually use my brain for tasks like "What should I eat now?" or "Cool, that thing is purple, where can I get that?"" ~DasBloody | "I let the dragon eat the forum" ~Idler | "and don't quote this" ~pinkydash

"You can find my IQ on the part of the bell-curve where the y-axis value approaches zero."

2,745Member, Friendly, Conversationalist ✭✭✭Let x=0: If I use a variable, I can do algebra with it.

1*x=0 && 2*0=0: therefore=>

2*1*x=0=1*x:

2*1*x=1*x:

2*1*x/x=1*x/x: =>

2=1;

much like you can't divide zero by zero you can't multiply 1/∞ by ∞ ∞ certainly isn't a real number, but that doesn't mean it's not really a number (just like i isn't a real number but is still a number). ∞ is also not merely a placeholder for a super big number; ∞ is a representation of an infinite or limitless quantity,

There are many systems that deal with infinitely large numbers, some of them (like the extended real number system) use ∞ as a number. Really, whether ∞ is a number depends on the number system you choose to use.

Typically though, using ∞ as a number is an abuse of notation, but if one is careful it can be a rather useful one.

Boots, Brogues, Cleats, Clogs, Flip-flops, Flippers, Galoshes, Getas, Loafers, Oxfords, Mukluks, Moccasins, Pumps, Sandals, Skates, Shoes, Slippers, Sneakers, Socks, Slingbacks, Stilettos, Rollerblades, Tennies, Waders, Wellingtons1,692Member ✭✭✭"After all, to the well-organized mind, death is but the next great adventure." -A. Dumbledore

"If you want to know what a man's like, take a good look at how he treats his inferiors, not his equals." -S. Black

“Confidence is ignorance. If you're feeling cocky, it's because there's something you don't know.” -Foaly the Centaur

4,177Member ✭✭✭✭✭What the freak is all this?

Steam Profile/Osu! Profile/Newgrounds Profile/YouTube Profile (soon™)Location:: Things /Likes: Other ThingsDislikes: Busy, Lazy and Crazy,About Myselfwith a spoonful ofhoney.: Interested in reading this. I can't believe it.About YourselfMom, get the camera!:Quotes"10/10 would create more alts to give more awesomes"-Frey /"I'm too lazy to create a quote"-Frey /"Make the future good by making the present better"-Frey(\n3n/)

6,436Moderator, Friendly, Helpful, Flagger Mod5,558Moderator, Friendly, Helpful, Flagger, Conversationalist Modapproximates0, but once you start using the "=" things change. That's the thing, n/∞=0 isn't a rule. lim[x->±∞](n/x)=0 is a rule. ∞/∞ is disallowed because ∞ doesn't always equal ∞. Indeterminate forms are forms that involve playing with limits where just replacing the parts of an equation with their limits doesn't tell you what the whole thing equals.For instance, lim[x->∞](x^2/x); lim[x->∞](x/x); and lim[x->∞](x/x^2) go to ∞, 1, and 0 respectively, even though lim[x->∞](x)=∞, ∞/∞ is, in this case, 1. I am allowed to simplify out the ∞ because I have already proved that it equals itself, therefore I am using the "lim[x->∞](x/x)" definition of ∞/∞.

You can't divide anything by zero--in fact, [Newton/Leibniz] invented calculus just to get around this problem--but if you are playing with variables, you can simplify them out of the equation, regardless of what the variable equals. (<--If you disagree with this, you disagree with Calculus)

<blockquote class="UserQuote">

There are many systems that deal with infinitely large numbers, some of them (like the extended real number system) use ∞ as a number. Really, whether ∞ is a number depends on the number system you choose to use.

Typically though, using ∞ as a number is an abuse of notation, but if one is careful it can be a rather useful one.

I understand that ∞ is really a number, but not in a typical sense. I agree that generally using ∞ as a number is an abuse of notation; I was trying to show this by abusing the hell out of it. My point was that--outside of limits--you can't treat ∞ as a number/variable and expect to have any sort of consistency in your number system; a point I was trying to illustrate by treating it as a number in 1/∞=0.

As for your first point, I agree that it depends on which number system you are using, so I will not debate this point further, it is a mere difference of opinion.

(I swear this argument would be so much easier if it were in person and I were allowed to talk using my hands and a chalkboard. You would see that I agree with you on every point

exceptn/∞=0. You can only do such abrupt things with ∞ if you are evaluating limits. This is because when you are evaluating limits, you aren't using "=" as "is equal to", you are using it as "approaches". Limits were invented because you can't actually allow ∞ to be used as a number.lim[x->∞](n/x)=n/∞=0

but n/∞≠0)

"10 variants of "I'm a platypus in a human body and only basic sexualities? Meh…" ~Shylight

"You might have me confused for someone who is clever and not lazy." ~Tellurium

"You can find my IQ on the part of the bell-curve where the y-axis value approaches zero."

4,188✭So different from this hell I'm living

So different now, from what it seemed

Now life has killed the dream I dreamed

5,558Moderator, Friendly, Helpful, Flagger, Conversationalist Mod"For all points in the complex plane, the chart is the identity map from the sphere (with infinity removed) to the complex plane. For the point at infinity, the chart neighborhood is the sphere (with the origin removed), and the chart is given by sending infinity to 0 and all other points z to 1/z." Wolfram MathWorld

While this allows you to play with ∞ as though it were a real number, it isn't. The sphere works because z/0≣ for , and z/≣ 0 where is complex infinity, is the Extended Complex plane, and ≣ is "defined as". So, yes, within the extended complex plane you are allowed to divide by ∞ by definition, but you are also allowed to divide by 0. I would consider that cheating if it weren't for the fact that the entirety of math rests on the backs of turtles.

Fun Fact: Bertrand Russell once wrote a 360-plus-page proof that 1+1=2.

In other news, here are some definitions of/including infinity as stolen from Wolfram MathWorld. (I have spent the last 2 hours on this site like it was YouTube or Wikipedia.)

"Infinity is an unbounded quantity that is greater than every real number."

"The Cantor diagonal method is a clever technique used by Georg Cantor to show that the integers and reals cannot be put into a one-to-one correspondence (i.e., the uncountably infinite set of real numbers is "larger" than the countably infinite set of integers)."

"However, even though the formal statement 1/0=∞ is permitted in C-*, note that this does not mean that 1=0·∞. Zero does not have a multiplicative inverse under any circumstances."

"Surreal Numbers"

"10 variants of "I'm a platypus in a human body and only basic sexualities? Meh…" ~Shylight

"You might have me confused for someone who is clever and not lazy." ~Tellurium

"You can find my IQ on the part of the bell-curve where the y-axis value approaches zero."

4,188✭So different from this hell I'm living

So different now, from what it seemed

Now life has killed the dream I dreamed

5,558Moderator, Friendly, Helpful, Flagger, Conversationalist Mod*Spends an hour browsing Wolfram MathWorld*

*Realizes what time it is*

You, sir, have stolen a good deal of my free time, and I would like it back! :)

"10 variants of "I'm a platypus in a human body and only basic sexualities? Meh…" ~Shylight

"You might have me confused for someone who is clever and not lazy." ~Tellurium

"You can find my IQ on the part of the bell-curve where the y-axis value approaches zero."

2,745Member, Friendly, Conversationalist ✭✭✭Helpful link:

http://en.wikipedia.org/wiki/Extended_real_number_line#Arithmetic_operations

My point is more nuanced. ∞ being a number depends on usage. When you use it in lim([->∞](1/x), it's not a number. The normal usage of ∞ as taught in calculus class is such that ∞ isn't a number. But if you use it in extended reals, you can make it one. I generally get where you're at, and I agree there is a large amount of agreement here. My point is not that 1/∞=0 is a general rule for mathematics. Under standard calculus you're completely correct, this kind of thing only occurs when evaluating limits.

My point is there is such a formulation (extended real number system) where you can use ∞ as a number and 1/∞=0 is a correct statement, and that system is not inconsistent.

Edit: Quote pruning....

Boots, Brogues, Cleats, Clogs, Flip-flops, Flippers, Galoshes, Getas, Loafers, Oxfords, Mukluks, Moccasins, Pumps, Sandals, Skates, Shoes, Slippers, Sneakers, Socks, Slingbacks, Stilettos, Rollerblades, Tennies, Waders, Wellingtons4,188✭So different from this hell I'm living

So different now, from what it seemed

Now life has killed the dream I dreamed

5,558Moderator, Friendly, Helpful, Flagger, Conversationalist ModThe reason that the system works is because it defines rules for playing with infinity according to the laws of infinite limits. In fact, that is the primary use of the ERNL; infinite limits. You aren't allow to play the trick that I did with the ∞/∞=1, because ∞/∞ is still undefined.

You are saying what I was trying to say, but was unable to get across because I had been up for far too long.

"10 variants of "I'm a platypus in a human body and only basic sexualities? Meh…" ~Shylight

"You might have me confused for someone who is clever and not lazy." ~Tellurium

"You can find my IQ on the part of the bell-curve where the y-axis value approaches zero."

5,558Moderator, Friendly, Helpful, Flagger, Conversationalist Mod"10 variants of "I'm a platypus in a human body and only basic sexualities? Meh…" ~Shylight

"You might have me confused for someone who is clever and not lazy." ~Tellurium

"You can find my IQ on the part of the bell-curve where the y-axis value approaches zero."

6,436Moderator, Friendly, Helpful, Flagger Mod4,188✭So different from this hell I'm living

So different now, from what it seemed

Now life has killed the dream I dreamed

16,175Member, Flagger ✭✭✭✭✭✭Without 0, we'd have -1 + 3 equal, like, either 3 or 4...

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"If you want to know what a man's like, take a good look at how he treats his inferiors, not his equals." -S. Black

“Confidence is ignorance. If you're feeling cocky, it's because there's something you don't know.” -Foaly the Centaur