Topic: Infinite Trailing 9's

There is a mathematical controversy that you don't need to be a math expert to debate: the question of whether 0.999... (... meaning on into infinity) is equal to 1. This is accepted as fact in many math textbooks, and is accepted by virtually all mathematicians and teachers. It is the students who generally question it. Usually, it is do to the fact that they do not have a full understanding of the concept of infinity.

Below are three examples of how this works:
A simple algebraic problem illustrates the concept:
x = 0.999...
10x = 9.999...
10x - x = 9.999... - 0.999...
9x = 9
x = 1
Thus, if x = both 1 and 0.999... then 0.999... = 1.
(if a = b and b = c, then a = c)

Also, it is widely accepted that 0.333... = 1/3.
If 1/3 x 3 = 1, and 0.333... x 3 = 0.999..., then 0.999... = 1.

The third, and most profound explanation, is as follows:
For two numbers to be different, there must be a number in between them.
With 0.999... and 1, it is impossible to fit a number in between them. The only number that could do that is 0.000... with a 1 at the end. However, the very definition of infinity means it has no end. Thus, there is no last zero with which to put the 1 after, and so there is no number in between 0.999... and 1. Thus, they must be the same number.

What do you think?

I think this is no place for you to be asking for homework questions, and giving children headaches.

I never seen these before but too me it seems like the problem is your trying to multiply and subtract infinite numbers. That problem is kinda misleading since it looks like you're multiplying .999 by 10 when you are really multiplying infinite 9s

the problem i see with this one is you are saying "it is widely accepted that .333 = 1/3" when it technically is less than 1/3. I'm no math major or anything and am not an expert on this topic but these examples seem flawed to me and don't prove anything.

If you dealing with exact numbers, then no it's not. For simplicity's sake it can be rounded up to 1.

0.333~ is only shown as equal to 1/3 because it's the closest decimal.

It's shown as 0.999...

Of course, if you get ask to round it up to a 1dp then you're going to get 1.

Other than that, they are two different numbers.

My brain is heating up trying to find the real answer...

Does .999... × 10 really = 9.999.... ? I don't think this seems right, but I don't have a calculator, so I'm not sure.

Preserved for the ages.

I learnt more in two minutes reading this post than I did in two years of A-Levels.

99 goes great at the end of a username!

trailing 9s are a tricky concept. On the one hand, seeing that an antibacterial product is 99.99999% effective gives you the reassurance that you're safe from harmful germs, or seeing that a DNA test is 99.99999% accurate gives you confidence that whatever it says is the gods' honest truth. On the other hand, that micro-fraction of a percent gives them some legal wiggle-room when you catch a disease or when it turns out you're some kind of chimera and the kids you've borne are the product of your uterus' DNA and not the DNA from the blood sample you gave in the first place. In some ways, those trailing 9s may as well add up to a straight 1, but does that make them the same as a 1? Not IMO.

hm. Very good question. I see what you mean..
Personally, i still think they are different numbers though. I feel if you would truly multiply .999999999999999999999999... then it wouldn't come up the same as what you would multiply 1 by. But how would you multiply a number that is written to infinity?? You can't really put something at the end of it because there is no end!
Just my opinion.

Infinity isn't a number. I can't fit an amount between 42 and a delicious bacon sandwich, but does that make them the same thing? That would mean the answer to life, the universe and everything is a delicious bacon sandwich!

_{okay, bad example}

Also, did anyone else think this was a random JRPG before they clicked the thread? I am so disappoint. u___u

Yeah, I was thinking Chunsoft were gonna make a 999 sequel that was infinitely better than the original.

(Just ignore the fact the original already has a sequel coming up, and the fact that it was pretty damn good in the first place, and that joke DOES work. Honest.)

Wow, I have a 99 in math too! I should stop posting at 6 in the morning when I'm half asleep!
But I do realize it equals that now.

Wait until you get into some seriously higher level mathematics (calculus, imaginary numbers, other things Sheldon Cooper might mention, etc), and get back to me ... if your brain doesn't implode then.

Such an extreme amount of disagreement!
Infinity is a hard concept to grasp, and, no, it is not a number (at least not like other numbers). Apparently, though, the biggest hangup with accepting this is that most people think they have a concrete understanding of the number 1. If something gets thrown at it that seems to make it less understandable, they're quick to question it.
I used the simplest examples of it, and I'm pretty well convinced just by them. There are, of course, more advanced explanations.
Also, this works with other numbers, not just 1:
3.999... = 4
55.999... = 56
0.24999... = 0.25
etc.