326 replies to this topic

[kucalc]

All I have seen presented is some crackpipe math using non-real numbers as real numbers, and drawing fantasy conclusions from it.
Actually, presenting a non-real number (0.99999...) and then stating that is is equal to a real number (1), is nonsense by itself. And that is the bottom line.

the bottom line is that you are smoking crack. all numbers that are not imaginary are real. who was ur teacher? a monkey?

No, verena's teacher is his calculator :

Oh... OK, let's see if our Casios can provide us with an answer.

Too bad CASIO's can't provide the answer for this problem.

Do you believe what someone else wrote on the internet, as "proof" ?

so you are saying we should not believe you? are you not writing stuff on the internet and labeling them as "proof"?

Yeah, we shouldn't believe verena. He hasn't even shown a single reference which I have asked numerous times. He's just saying stuff like, "0.3333... is non real because it's just a approximation." or "0.99999... and infinity are non real".

you are a disgrace and embarrassment and you bring shame to the german people

Actually, looking up his IP, verena's ISP is somewhere in the east of the US. That would explain some of his jokes and remarks about Britain. If verena is a US citizen, I think it's people like him who give the US a bad reputation.

if i was your father or mother i would have you neutered so you cannot have children and to prevent more retarded people from being born

Lol, ok..... if I was verena, I'd check under the seat for some radioactive element (such as plutonium) duct taped to the bottom of his seat damaging his reproductive organs.

As for verena's proof, what can go past infinity? Nothing. This "proof" was already mentioned in this thread a couple of pages ago and was disproved.

Here is my proof that 0.99999... is less than 1:
(proof start)
You know that 0.9 + 0.1 = 1, 0.99 + 0.01 = 1, and that 0.9999999 + 0.0000001 = 1, etc.
As you add nines to the first term of this equation, you insert zeroes into the second term of the equation. The sum always being 1.
As certain as you will NEVER reach infinity (keep adding nines) you will ALWAYS insert zeroes and there will ALWAYS be a little difference between 0.9999..... and 1.
(proof end).

So, you somehow surpassed infinity and were able to put a 1 after infinity zeroes? To say something like, is like claiming that you are more powerful than the creator of the universe, which you are obviously not. Either, only someone with a large ego or is just plain stupid would claim that. Answer this, how could someone place something after infinity? You can't, therefore that "little difference" cannot exist. To say that there was, would then mean that 0.999999... stopped somewhere, which it doesn't because it always keeps going forever.

In all of your examples, you had to stop or limit the number of zeros in order to place the 1. If you have infinity 9's, you have infinity 0's, which is why your proof doesn't work:

You know that 0.9 + 0.1 = 1, 0.99 + 0.01 = 1, and that 0.9999999 + 0.0000001 = 1, etc.

Infinity does not stop and can never be reached. To prove this to you, I want you to do this now, write infinity 0's. Write them out by hand, one by one, on paper. Keep doing it until you reach infinity. No cheating (such as using the .....). Here, I'll give you a head start, 0.00000000000000000000000000 Now you just have infinity more zeroes to write. After you have written infinity zeroes, see if you can write the number 1. Impossible, isn't it? The 1 is never reached. You can never surpass infinity. Thus you are still proving 0.9999999.... equals 1.

Perhaps, I should officially close this thread with the conclusion that 0.99999999...... equals 1. No proof yet still exists showing 0.9999999.... does not equal 1 for centuries. Most of the world (if not all, except for verena) accepts 0.9999999... as the equivalent of 1.

[verena]

OK I admit that I have said some things that were not very nice, and also several things that were mathematically incorrect. I apologize to the English people for my racist remark that they have a good sense of humour. Also sorry Mr. Wolfram if I involved you with anything that was not your doing, and used you to ridicule a so-called definition of zero. It was just the way that kucalc presented you - the unquestionable authority.
By the way, ln(0) is undefined - plenty of references.

I am happy to present you with a rephrased proof that there is always a difference between 0.9999.... and 1. Just to clear things up, maybe kucalc you will understand this time and admit that 0.9999... is less than 1.

Here is my proof that 0.99999... is less than 1:

(proof start)

You know that 0.9 + 0.1 = 1, 0.99 + 0.01 = 1, and that 0.9999999 + 0.0000001 = 1, etc.
Each time you add a nine to the first term of this equation, the second term (the difference between the first term and 1) gets divided by 10.
As certain as you will NEVER reach infinity (keep adding nines) you will ALWAYS keep dividing by 10 and there will ALWAYS be a difference between 0.9999..... and 1.
And as everyone knows, if you divide a number by 10, the result is a 10 times smaller number. Repeated divisions by 10 will always result in a number that is 10 times smaller - NEVER zero.
(proof end)

As there is always a difference between 0.9999... and 1, 0.99999... is less than 1.

In kucalc's form of math, repeated divisions by 10 eventually, at "infinity" result in exactly zero. (Now, can we reach infinity, or not, I wonder ?)

Why then does kucalc's 'proof' seem true on first sight? Her trick, as detailed in her post above, is to just use "infinity" zeroes to eliminate the difference between 0.99999... and 1, by sending it into the impossible zone beyond infinity. Start with 0.1, then 0.01, 0.0001 etc. and once there are "infinity" zeroes inserted between "." and "1", *POOF* the "1" is gone, because "beyond infinity" is impossible. Math is like magic.

However Kucalc, thank you for repeatedly straightening me out, math wise. I understand your anger and frustration because it is not every day that something you believe in gets undermined and ridiculed, especially by someone who only remotely knows what he is talking about. I suggest you direct your energy towards the study of numbers, the different kinds of numbers, and the history of numbers. Really, fractions were used before decimals, not the other way around. Oh, 'limits' is a nice subject too, one of my favorites.

I learned a lot from this exercise, having to look up things and refreshing my math. Maybe I should become a math teacher now, because there is a lot of nonsense going around.

[verena]

(quote MM) 1) u r now also a liar. you never said they had a good sense of humor.
DARN you're right - I said that they have a bad sense of humour. Sorry again.

Now ladies, here is my proof that 0.99999... is less than 1:

(proof start)

You know that 0.9 + 0.1 = 1, 0.99 + 0.01 = 1, and that 0.9999999 + 0.0000001 = 1, etc.
Each time you add a nine to the first term of the equation, the second term (the difference between the first term and 1) gets divided by 10.
As certain as you will NEVER reach infinity (keep adding nines) you will ALWAYS keep dividing by 10 and there will ALWAYS be a difference between 0.9999..... and 1.
Everyone knows that if you divide a positive number by 10, the result is a 10 times smaller number. The result is NEVER zero.
Therefore, as there is always a difference between 0.9999... and 1, 0.99999... is less than 1.
(proof end)

Only in kucalc's 'infinity', the repeated divisions by 10 result in a zero.

Now what's wrong with this proof ? Bring it on ! Prove me wrong !

[kucalc]

DARN you're right - I said that they have a bad sense of humour. Sorry again.

Ok.....

Now what's wrong with this proof ? Bring it on ! Prove me wrong !

With pleasure.

You know that 0.9 + 0.1 = 1, 0.99 + 0.01 = 1, and that 0.9999999 + 0.0000001 = 1, etc.
Each time you add a nine to the first term of the equation, the second term (the difference between the first term and 1) gets divided by 10.
As certain as you will NEVER reach infinity (keep adding nines) you will ALWAYS keep dividing by 10 and there will ALWAYS be a difference between 0.9999..... and 1.
Everyone knows that if you divide a positive number by 10, the result is a 10 times smaller number. The result is NEVER zero.
Therefore, as there is always a difference between 0.9999... and 1, 0.99999... is less than 1.

Your saying that 0.1/10 = 0.01, then 0.01/10 = 0.001. The problem with this is that you've jumped over infinity and now 1 has been reached. You've somehow managed to put a 1 after infinity zeros? According to you this "difference" is 0.00.....1? Now, that's a non real number. That number self contradicts itself, having infinity zeros, but simultaneously stopped by the digit 1? No digit can be placed after infinity as infinity is never reached. Your proof has just shattered into infinite of pieces of glass. If you think that's magic, you haven't seen infinity. It goes on forever.

In fact, the division by 10 can only be used to prove 0.99999.... does equal 1, by taking the sum of the infinite series 9/10+9/100+9/1000+.....:

And guess who came up with that proof? Ever heard of the famous Swiss mathematician, Euler? I'm sure you have. He came up with that proof in 1765 and published it in his book Element's of Algebra. You should take a look at his book.

Also check out Bonnycastle's textbook An Introduction to Algebra written in 1811, where he also has a proof showing 0.999999... equals 1.

Fractions and what you call, their "decimal approximations", still don't convince you? What about square roots? Can't argue with that. Let's take the square root of 2. The first couple of digits of the square root of 2: 1.41421356. Now square it: 1.41421356^2 = 1.99999999. Hmmm, how about we go further? : 1.41421356237309504880^2 = 1.99999999999999999999. Coincidence? Nope. You'll see that 1.4142135623.....^2 = 1.9999999..... Thus 1.99999999.... equals 2. No fractions and their "decimal approximations" involved.

I'm going to take TacoFred's suggestion a couple posts back on that further discussion for this topic should be stopped. I think it's now time to close this thread, as there is overwhelmingly too much proof that 0.999999... equals 1, as yet no concrete mathematical proof exists for showing that it's false. The polls have remained in favor of Yes for 0.999999... equals to 1 for years. Plus we always are getting the same proofs over again and again for proving 0.9999.... = 1, with some fantasy proofs "what if I add 1 after infinity digits?", combined with trolling, flaming, personal attacks and derailing of topic.

After more than 4 years of discussion: 0.9999999999..... equals 1
Now feel free to move on with your life, perhaps doing something exciting and adventurous that you've always wanted to do in your life...

[2072]

(proof start)

You know that 0.9 + 0.1 = 1, 0.99 + 0.01 = 1, and that 0.9999999 + 0.0000001 = 1, etc.
Each time you add a nine to the first term of the equation, the second term (the difference between the first term and 1) gets divided by 10.
As certain as you will NEVER reach infinity (keep adding nines) you will ALWAYS keep dividing by 10 and there will ALWAYS be a difference between 0.9999..... and 1.
Everyone knows that if you divide a positive number by 10, the result is a 10 times smaller number. The result is NEVER zero.
Therefore, as there is always a difference between 0.9999... and 1, 0.99999... is less than 1.
(proof end)

I just wanted to point out where the misconception of Verana comes from: notice the words I put in bold.

Time is a human concept, not a mathematical one.

you don't "keep adding" nines until infinity. there IS an infinite number of nine.

Verana: Did you ever thought about the universe and its infinity? Try, it's a strange feeling, like if your brain tries to divide something by zero... Human brain have difficulties with infinity it doesn't seem natural ; but it is.


It's strange because this thread, and especially the last posts, remember me of the thread about the Bush election and re-election. Some people are so much sure and convinced of something that even with a thousand of proofs you can't show them their mistake... I wonder...