Math Is Fun Forum

So your argument is that C MUST not be equal to C + D because 0.999... is not equal to 1, so C must be < 1, meaning that 0.999 is not equal to 1. The problem with this is still the second step... you're assuming 0.999... is not equal to 1, and using that to support your proof that it isn't. You can't just use an assumption to support a proof of that assumption, you must first prove it to be true. If you drop the assumption, then C can equal C + D for cases where D = 0, therefor C + D = 1 = A, if D = 0 then C = A.

Recurring - A recurring decimal (or "repeating decimal") is an expression representing a real number in the decimal numeral system, in which after some point the same sequence of digits repeats infinitely.

Okay, I did some reading and learned that numbers originally come from Sumeria, between 8000 and 3500 BC. About 3100 BC they invented the concept of abstract numbers that don't represent specific items. Originally they were made of small clay tokens, but they gradually became markings made with a round stylus at different angles, to represent the different numbers.

Now although I find the history lesson fascinating, I'm sure that you didn't mean for me to study 10 000 years of numerical history to understand why you're multiplying 0.9 x 4 as part of a proof that shows there's a 10% difference between 3.6 and 4.0, which somehow represents that 0.999... is less than 1. But the problem is that I'm not sure what else you could mean by "where numbers come from and how they're made". Why does a number have to come from somewhere? Where does the number 1 come from? What about 0.9? What about 4? Does it matter where these numbers "come from"? We all understand what they represent, right? Or do we have to start this conversation with a proof of the relationship be 1 and 2, and why 3 <> 2, 3 > 2 > 1, and where does 4 fit into this odd series of symbols?

Then why don't we just ask a Moderator to change the title of the thread, instead of starting yet another new one?

Do you need to use all 4 numbers? If not, it's pretty easy, just remember that dividing a fraction is like multiplying by it's inverse (so 4 / 1/6 = 24)

If you need to use all 4, obviously the 1 is easy, but working in the 3/8 is a bit harder...

I never used a sentence, I always just remembered it as Soh Cah Toa (sounded out as 3 words), and found that easier than trying to remember that Sally Only Hates Cars And ... (whatever silly pneumatic you can come up with). Or if you have trouble remembering Soh Cah Toa, try "Sock it To ya!" (same thing, just translated into real words)

By "sister thread" I think he meant that he'd also close the "proof why 0.999... = 1" thread that you created your thread in retaliation to. Now both are closed, and all of the discussion about this should continue on this thread alone.

I wasn't using fractions, I was expressing a division of 1 divided by 3 * 3 (the same way you were dividing 1/0.9 * 0.9). Yes, my 1 divided by 3 = 0.333... is a repeating value, the same way that your 1 divided by 0.9 = 1.111... is a repeating value.

There you go on about the "single value" again, which I still don't understand or recognize as any valid math theory. I really have no idea what this last sentence of yours means (or should I say sentences, since there seems to be punctuation randomly in the middle of it).

Lol, that's funny... all this time debating and I never even thought to try punching that formula into windows calculator. I just assumed that it rounded to 32 digits (although that's impressive in itself) and would give the 0.999... result for the formula. Apparantly it's smarter than I gave it credit for, with regards to infinitely repeating decimals. ;-)

Umm... read the first line of my reply above. "I'm not arguing against the idea that 1/0.9 * 0.9 = 0.999..., I completely agree with that. "
So I agree with you that A/B * B = 0.999..., I just also happen to believe that A/B * B = A = 1, which means that 0.999... = 1

Sorry, I was looking at the wrong B. But you still didn't respond to the rest of the issue I had with your formula, just managed to pick up on the one inconsequential comment that I made and was wrong about.

B doesn't "become" 0.999..., B is still 0.9, C is 0.999...
Using your logic I could just as well say "in your fomula, A starts equal to 1, and then by being divided by B and then multiplied by B, A becomes equal to 0.999..., proving that 0.999... = 1"

What? Numbers can't "start <1 and somehow become >= 1". A number is a number, and doesn't change in any way. So of course I can't show you a number that magically changes. The problem seems to be your belief that 0.999... starts <1, which it doesn't. 0.999... = 1 at all times, it doesn't start <1 and become =1, it is simply = 1. And don't say "but it starts at 0.9" just because those happen to be the first couple digits of the number, because that doesn't mean anything at all. In mathematics, there is no such thing as a "single start value" that is equal to the first few digits of the number. A number is equal to what the number is, it is in no way equal to what the first few digits are (unless it's only those digits). I'm not sure how many more different ways I can try to make you understand that.

I'm not sure I see your logic here... just because 1 < 9, 2 < 9, 3 < 9,  4 < 9, 5 < 9, 6 < 9, 7 < 9, 8 < 9, doesn't mean 9 < 9... you can't just create an arbitrary logic pattern and assume that it continues. Sorry, you need better logic than that.