Defining inifinite [Bad spelling, yes, but I felt like preserving the original. I hope this doesn't spur any grammar-geeks...] as a number followed by an endless stream of zeroes before the decimal point. [Yes, that wasn't a complete sentence. Will you not go grammar-geek on me now that I've acknowledged that?] That is, infinite = 1 0 . 0 [There's supposed to be a bar over the first 0, (placed there using an unbreaking space) but my comments mess all this up] (the decimal point and the zero after it are just for demonstration and could be removed at your discretion, and the bar is signifying an endless number of that digit following the number to the left). So, with this definition, we can create this proof:

(Just a side note: I can define the number infinite, because there aren't any properties surrounding it, except that it is not smaller than any number, which my property satisfies, which is hard to show now, so I'll do it later on. [I'm sure I figured out a way somehow later on in that thread. I also got another way to arrive at 1/0=∞ in the threed (from now on, for ease of reference, the thread where this proof originates shall be called, the threed) later on, but it involved dividing by zero, so it was just a bit problematic...] Also, we cannot just create a definition for raising to the power of 1/2 that sets it equal to square-rooting, because that would violate its property that it is the inverse of squaring.) [The square root example comes from the fact that the post this came from also discussed raising to the power of a half] [Okay, I admit now that I can't just say one followed by infinite 0's is infinity, because I haven't proved that it satisfies that sole property of infinity, but 1/0 is at least some number, and I'm sure I could pull together a proof that this number is even ∞, but let's just start with saying that it at least isn't undefined]

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0 . 0 = 0 Adding zeroes, even an endless amount of zeroes, after the decimal point will not change the value of a number

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0 . 0 1 = 0 . 0 *** Sorry, I don't know the name of the property. [This comes from the fact that 1=0.999999999..., so therefore 1-1=0 implies 1-0.99999999...=0, which you can 'simplify' to 0.00000000...1=0. I hope I'm not practically begging for this thread to be closed by discussing a topic closely related to 0/0 and using the fact that 1=0.99999999... in a proof]

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0 . 0 1 = 0 Substitution Property of Equality

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( 0 . 0 1 ) ^ ( - 1 ) = ( 0 ) ^ ( - 1 ) "Operation" Property of Equality (performing an operation [What I mean to say is "the same operation," but you get what I mean anyways, right?] to each side of an equation will preserve the equality)

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1 / 0 . 0 1 = 1 / 0 Property that states x^(-1)=1/x

***if you would like to see the proof for this, just ask, but I am assuming you already know because it is the foundation for turning fractions into decimals and vice versa [Oops, forgot a period there. Anyways, I guess I already showed you all the jist (Is that how you spell that word? Oh great, grammar-geeks are gonna spam this thread...) of the proof anyways]

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Now, we must find out what 1 / 0 . 0 1 is. So, an interesting property is that 1/0.(n)1 = 1(n).0 * 10, where n is a number of zeroes. For example, 0.0001 has 3 zeroes, so 1/0.0001=1 followed by three zeroes times ten, or 1000.0*10. We can use this right now, and since we know that our number is followed by an infinite number of zeroes, 1/it will get a number followed by an infinite number of zeroes before the decimal point (hmmm... sounds familiar) times ten.

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1 0 . 0 * 1 0 = 1 / 0 Aforementioned property

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But, wait, what about that nasty times ten in there? Hmmm... Well, since 0 . 0 1 = 0, and 10*0=0, then 1 0 * 0 . 0 1 = 0 = 0 . 0 1! <-Not factorial operator [Yes, my tone does get a little less 'official' around this point]

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0 . 0 1 = 1 0 * 0 . 0 1 Multiplication property of zero

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1 / ( 0 . 0 1 * 1 0 ) = 1 / 0 Substitution Property of Equality

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1 / 0 . 0 1 / 1 0 = 1 / 0 Dividing by multiplying property, or whatever it's called

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1 0 . 0 * 1 0 / 1 0 = 1 / 0 Aforementioned property

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1 0 . 0 = 1 / 0 Inverse Property of Multiplication

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1 0 . 0 = infinite Given/Definition

infinite = 1 / 0 Substitution Property of Equality

1/0 = infinite Reflexive Property of Equality (Just to make it look nicer)

Now, this proof has some major implications. For starters, where k is any complex number (excluding infinite), k*infinite=infinite, because k*infinite=k*1/0=1/(1/k)*1/0=1/(1/k*0)=1/0, because

0*(1/k) = 0*(1/any complex number, given k != 0, because 1/0 is not a complex number according to our definition) = 0. In fact, 0*infinite is indeterminate, [Please just ignore this if you're out to have a fight about 0/0, or if you're a forum admin looking 24/7 to close any post with the term 'indeterminate' in it] because since k*0=0, 0*infinite=k*0*infinite=k*0*1/0, so since k*1/k=1 (Give me a proof showing this is untrue when it comes to infinite and 0 and I'll try to disprove it or I'll offer an explanation for why 1/0 still = infinite. I think proofs "demonstrating" this exception to be "true," thus showing this notion of infinite breaks the laws of complex numbers (even though infinite isn't even a complex number in some rights) and meaning that infinite can't be 1/0, are a large part of the reason why people don't believe 1/0=infinite) [this idea of me disproving your disproof is discussed more in the little bunch of text after this quote], 0*infinite=0*1/0=k*0*1/0=k*1=k, and since k is any complex number (it can be zero this time), infinite*0 ends up equalling indeterminate. In fact, 1/0 equalling infinite doesn't even violate either the property that k*0=0 or that 1/k*k=1, because 0*infinite=0 has an infinite number of solutions, one of them being 0, and another being 1. [This concept of getting multiple 'solutions' (yes, I use that word loosely here, but so many other people use it this way too that it's become math-slang) is a recurring idea in my mathematics of infinity. In fact, if you create a disproof of 1/0=∞, most likely it has something to do with multiple solutions that makes it invalid.] Moving on, we can see that infinite^l=infinite, [Why'd I use 'l'? It's such an irregular letter...] where l is a non-infinite rational number, because infinite^l=(1/0)^l=1^l/0^l=1/0. Now to show that my definition of infinite is not smaller than any number. Well, my proof for this isn't that concrete, but once you go infinitely far out from the number line, there's no way to measure how big a number is. [Technically, once you get an infinite distance from the number line, every number is infinitely large.] If you add 1 to the definition of my number, you get this:

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1 0 1 . 0 / 1 0 [The divided by ten is because I moved things to the left to make room for that one. I see a problem with this, though: I'm not adding 1, I'm adding 0.1. I can just say I'll do that ten times and it'll get adding one.]

If you keep on adding one to the point that you've added an infinite number of ones, you get:

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1 0 . 0 + 1 0 . 0 [See, not quite the most concrete proof. But still a way to communicate the concept.]

Which equals the number before adding all those one. Of course this could be wrong, because we are only assuming that adding one infinitely should increase the number. [See? I told you it wasn't the most concrete proof.] The meaning behind the fact that you can't just add 1 to increase the size of the number is that you can't create a number greater than infinite. [That sentence seems out-of-place... Oh well, but it conveys an important point about my definition of ∞.] Oh, and how do we even know if infinite is positive? Well, it's both positive and negative in a way, because infinite=-1*infinite=-infinite. Strange. [It's like i: neither positive nor negative.] Well, we know that a positive over a positive is a positive. And, a negative over a negative is a positive and a negative over a positive is a negative and a positive over a negative is a negative, and then a zero over a positive is zero and a zero over a negative is zero and a zero over a zero is a positive,zero, or a negative, [Once more, since this is post just contains tiny references to 0/0, it's not bad. As long as no one starts an indeterminate internet post war. Then, the value of this discussion would become indeterminable.] but then when we divide a positive or negative by zero, what do we get? We get an infinite, [which is neither a negative nor a positive (nor zero) (in a way)] a now defined infinite, and a very strange one, too.

First of all, I would like to acknowledge that my way of proving it isn't the strongest, but most of my belief in this comes from the fact that the disproofs I've seen demonstrating the impossibility of 1/0 are wrong, and from the fact that 1/0=∞ makes for a more complete mathematical language. I can't create rebuttals in advance to every disproof all of you might come up with, so I'll just leave you all to post your own reasons for why I'm wrong. (Because you all totally weren't going to do that if I hadn't told you to). It would a good idea to read through the thread in the url above. It obviously wouldn't be worth your time to read through all of it (not only is it big, but it's math-y, too, even if it is mostly just space and quotes). Just skim through to get the general idea of what I mean. Of course, you don't have to (especially if you're already burned out from the quote part of my proof), but doing so would make you better-informed about my reasons for my opinion and the topic at hand. Well, anyways, have a Happy Friday (or Saturday, depending on your time zone)! Bye!