A friend of mine brought this up, as it is a debate going on right now in the worlds of science and math. Basically, the argument is that a decimal fallowed by an infinite number of nines is actually equal to One.
But this is all well and good for the world of Math. But science has proven a different logic, were they are not equal. My favorite example is that in science, one plus one is approximately two, due to the impurities of one. This expression basically is stating that having two halves put back together does not make it whole again.
So in my argument, I argue that if 0.999... is equal to 1, then 1 is equal to 2. I shall demonstrate using the same logic. I shall refer to an infinite amount of numbers using "..."
Yep, basically what Agent said. On your first post, you're right until you get to step one. Actually, you're kind of wrong before that. Really, your main logic flaw is in step two. "Step 2: 0.000...001 + 0.000...001 = 0.000...002
2 / 1 = 2 0.000...002 / 0.000.001 = 2" 0.000...001 is the same thing as 1/infinity. So is 0.000...002. 0.000...002 / 0.000...001 != 2. It equals undefined. They're the same number, just written in different ways. They're both the smallest number possible without reaching 0. Because between any two numbers, there has to be another number, 1/infinity = 0. Currently, 0/0 is undefined. != is Does not equal, by the way.
As for the other errors, see this Wikipedia page and scroll down to Fallacies Based on Division of Zero.
.9999999999999999999 is not equal to 1 and never will be. Have you ever thought they were just rounding it to a whole number to make it easier? WHich one is more simple?
Okay, first things first, gotta get this out there... Mind = Blown. That's my first math equation.
My second thought to this debate, 0.999 does not equal one. It is equal to the fraction 999/1000 NOT 1000/1000 (Which is simplified to1/1. Thus .999...999 does NOT equal ONE.
This is amusing, simply for the fact that saying 0.999... != 1 is considered a form of trolling in certain parts of the internet. Why? Because it starts the same long-winded debate between the ones who use proofs and the skeptics who say it is not the same because it does not look the same.
My second thought to this debate, 0.999 does not equal one. It is equal to the fraction 999/1000 NOT 1000/1000 (Which is simplified to1/1. Thus .999...999 does NOT equal ONE.
Your logic does not follow. You're just saying .999... * infinity/infinity (the exact same orders of infinity) is not equal to 1, which is essentially saying "0.999... != 1 because it isn't." Which isn't a very good proof.
Silver, we're not dealing with .999, .999999999, or .9999999999999999. We're dealing with .999.... .999... is infinitely close to 1. 999/1000 is not infinitely close to 1000. Nor is 999.99999999. However, 999.99999... is. If a number is infinitely close to another number, they're the same thing.
Barack, it's the same issue. We're not going from 33 to 1/3. We're not going from 33.333333 to 1/3. We're going from 33.3333... to 1/3. 33.333333... is infinitely close to 1/3. Therefor, it's the same number.
The credible answers that I have received on this mater are as follows:
1: Infinity does not exist in algebra or mathematics. It only exists in Calculus were we can only approach it, aka limits.
2: You can not use different worlds of math in the same formula, aka, decimals and integers.
3: The reason why you cannot divide by zero is because it gives funky results like 2 = 1. Unless you are dealing with nuclear physics were it's actually appropriate to divide infinity by zero as you are dealing with light speed and all that jazz.
This is speculated, not proven. 1 does not equal 2. Find 1 instance without using 0 as an outcome that makes it equal. Also, 1.11111 equaling 1.11111 is wrong as it is rounded down, not up. What you're proposing is infinity. 1 = 2 = 3 = 4 etc. 3/3 proposed as .9999 and 1 is like 0/0 being proposed as 0 and 1. What? Now all of a sudden 0 = 1 = 2? Infinity is a touchy matter. The argument stems both ways. The problem with math is its usually just a definite answer. Only 1 answer is allowed. I feel that if Mathematicians opened their minds a little more than they could possibly accept the fact that everything may (or may not) have more than 1 solution to a problem.
ok like you said talo, there are limits. .9999....999 can never equal one, because infinity doesnt exist. you can never get to infinity. due to the limits, .999...999 can never reach one, because that is as close as it can get to one without actually being one. otherwise, .999...999 would actually be known as 1.
deth4, you're looking at it all wrong. It's not .9999 equaling 1. 3/3 does not equal .9999. It equals 1. 1 equals 3/3. .999 is not involved. The point of view you guys are viewing it is that 1/3 equals .333 so 3/3, you HAVE to multiply the decimal value by 3. But according to the first post, 1.111 equals 1.1112 so .333 equals .33334 so it would be 1.0002. Not .999 so completely disproving Talo's logic. I see it as 1/3 equals 1/3. .333 equals .333. .999 equals .999 and 1 = 3/3. Simple right? No need to over complicate. Also, one more note. Infinity is not proven therefore not disproven and can never be. Infinity is a concept, not a fact.
