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Those proofs only prove that our system of math is fundamentally flawed when it comes to dealing with infinite numbers.Quote:
Originally Posted by yasunobu13
Only the number that should represent the quantity 1 is the number 1.
1 = 1
0.999... = 0.999...
0.999... < 1
1 > 0.999...
There are no infinite numbers there. Do you mean repeated decimals? Just because a number can be represented in more than one way doesn't mean that anything is flawed. It would be flawed if the same number represented in different ways could create different mathematical results.Quote:
Originally Posted by random25
Since that is not the case, mathematics is sound in this respect. You can use 0.999... in any calculation where you can use 1 and get the same result.
20 + 1 = 21
20 + 0.999... = 20.999... = 21
Just because you want it to be different doesn't mean that anything is flawed.
saying 0.999... = 1, is just as wrong as saying 0.999... = 0.999999999.
numbers are just labels representing amounts.
1 = 1
0.999... = 0.999...
a = a
b = b
apple = apple
orange = orange
honestly I'm no math expert, i just like to argue.
You have yet to show me anything that will make me believe that our math system is not flawed and 0.999... = 1.
OK,
Prove to me that i really exist and i will admit that 0.999... = 1.
GPS and RelativityQuote:
Originally Posted by swak
Random, proving that you exist and proving that 1=0.999... are two completely different things. The first one is a philosophical problem that takes nothing for granted and questions the existence of the entire world. I can't prove that I'm not just a brain in a jar receiving data from some computer making up the world I'm lining in. I could question the existence of everything (except myself, according to Descartes, including myself, according to others), even free will.
The second statement is based on some axioms. Its a scientific/mathematical statement, which means that it assumes the world we live in is real, and if it is not, then it simply tries to understand this, virtual, world. I won't get any of the math 'more' correct if I start questioning the reality of the world we live in, so I won't be bothered. I'll just assume that it is real, and that everything that I interact with is also real. If things are not real, then I'll pretend they are, because it will help me understand the world.
To prove that you exist means that I have to base my logic on axioms, but if I doubt you exist then I can also doubt everything else I have observed in my lifetime, and proving anything will be impossible. For the math question, I base my proof on observations that I have made (if you have a coin and I have a coin, then we have two coins in total). If I try to prove your existence, then I have to give up on the math proof until I have proved/disproved your existence. Since I can't prove your existence without first dying (assuming I will go to another world from where I can observe this world), I will base my mathematical proof on (my assumption of) your existence. If you claim to not exist then nothing in the world can be certain, and there is no point in living.
Conclusion: As much as it/you bothers me, I just have to assume that you exist.
It's not flawed and it was shown in the first post of the thread. You still have yet to say what is wrong with the proofs.Quote:
Originally Posted by random25
Numbers can have different representations but still be equal.
3.5 = 3.5000000 = 35*10^-1 = 7/2 = 35/10
Your only argument seems to be that it feels wrong. An argument based on intuition, not facts. It's really not that hard, just tell me why the proofs are wrong. This is what, the 6th time I've asked? And still no response. Makes me think you're not even reading these posts.
Is this really a response to disprove mathematical evidence?
"Those proofs only prove that our system of math is fundamentally flawed when it comes to dealing with infinite numbers."
'I don't like it, so hundreds of years of work by billions of people must be wrong'
It seems the whole thing is dependant on accepting that 0.333... is a real number. It's not imo, it's a map, it's an idea, it's undecided.
Quote:
Originally Posted by wikipedia
Listen...
1/3 is an idea. It's not a number, and it can't be applied to 1.
0.3333... is the closest numeric representation available to us when expressing 1/3, but it simply does not cut it.
0.33333333333 * 3 != 1.
Therefore 0.3333... != 1/3.
They are conceptually not on the same plane of reality. that's all there is to it.
Many fractions can cleanly be applied to the number 1. 1/3 can not.
Now stop the nonsense :)
I gave you the reason i am arguing:Quote:
Originally Posted by yasunobu13
1) your "proof" is based on math which was, as many of you may have already guessed, created by semi-evolved primates.
2)I am bored, and i like to argue with people on the interweb while i am bored.
OK, I'm done arguing,
I will now process this discussion logically.
I think i understand how to perceive the situation in the way you are referring. Heres a nice story to help out:
For three days three primates took one piece of food and split it evenly between themselves.
On the third day the primates had eaten a total of one piece of food each.
So one divided by three equals the fraction one third, 1/3 or 0.333...
and one third three times equals one.
So 0.333...*3 cant equal 0.999... it must equal 1.
The primates realized how surprising this was, and agreed that they should let everyone know. Immediately they began to alert the others of the situation over the interweb.
How about that?
I'm not sure about your second proof though, how could you even do that one if it starts of with 0.999...
No. 1.333... is an inadequate representation of the fraction 1/3. It's the closest we have (which is why this argument was started), but it is not the same. There can be no same. A fraction is an idea that is not bound by numeric logic. It's a different entity. You can't apply a number to it!
It's wrong. Wrong I tell you!
man. cant believe this thread is still going on.
i declare yasunobu the winner. now go home. :D
This reminds me of that old frog jumping thing...
If a frog jumps half the distance towards its target, does it ever reach it?
Of corse it doesn't. If the frog ever reached its target, that jump would not have equaled half the distance. It will forever be moving towards it, but will remain an infinitely small distance away.
The same is true for 0.999999999999999... You say it equals 1 because we can't figure out where else to place it. But you know there's a discrepancy there. It's intuitively obvious. Why is there 1, and also 0.999...? How can two numbers be different but the same? does 0.333333333... == 0.34?
oh and Flash Lackey...Home time is 6pm (my local time). I won't forget...
I think the first proof is wrong, if we are going to use 0.333... to represent one third of one, the proof should be:
1/3 = 0.333...
0.333... * 3 = 1
So how does 0.999... even come into the equation?
And the second proof,
If it starts off with x=0.999... how could the rest of the proof even be calculated?
Our system of math cant work with a never ending number such as 0.999..., so we would have to use 1 instead.
So shouldn't x actually equal "undefined" or "unmeasurable" or "infinite" from the start, not 1, there by proving that our system of math cant process an infinite number.
By saying 0.999... = 1 you are actually saying we cant do infinite math yet,
so instead of using a number that is almost 1, we are going to just go ahead and use 1.
And 0.999... cant actually exist because if it did it would automatically be 1.
3*3 = 9Quote:
Originally Posted by random25
0.3 * 3 = 0.9
0.333... * 3 = 0.999...
Why do you keep saying "infinite math" it's very confusing.Quote:
And the second proof,
If it starts off with x=0.999... how could the rest of the proof even be calculated?
Our system of math cant work with a never ending number such as 0.999..., so we would have to use 1 instead.
So shouldn't x actually equal "undefined" or "unmeasurable" or "infinite" from the start, not 1, there by proving that our system of math cant process an infinite number.
By saying 0.999... = 1 you are actually saying we cant do infinite math yet,
so instead of using a number that is almost 1, we are going to just go ahead and use 1.
0.999... is a number with a 0 before the decimal point and all 9's after the decimal point. Saying that it is not a number goes against elementary school math.
You can create the number in the same way you create 1/3 = 0.333... or are you saying all recurring decimals are improper mathematical entities?
Oh, so now you agree 0.999... = 1. That's a property of equality that I stated before. We can swap 1 into any mathematical statement that uses 0.999... can achieve the same result. They are just different representations of the same number.Quote:
And 0.999... cant actually exist because if it did it would automatically be 1.
Glad you finally came around. ;)
Foolish humans!
0.999... is a number smaller than 1 by an infinitely small amount! the 9s go on forever! 9 is smaller than 10! At what point do the 9s do their magic sneeze and tick over to a whole number?!
How could any mistake be made about this?
yasu, .333 repeating times 3 is not .999 repeating.
I can't believe this thread has been going for so long......
Christopher Mitchell
Three thirds equals 1, not almost 1 :rolleyes:Quote:
Originally Posted by yasunobu13
The "..." means that the number is followed by an "infinite" amount of 9s.Quote:
Originally Posted by yasunobu13
That makes it an "infinite number".
Trying to use our system of math on an "infinite number" cant work correctly.
0.999... could exist in theory,Quote:
Originally Posted by yasunobu13
but your way of thinking suggests that it is equal to one and not equal to one at the same time.
It has to be either 1 or not 1, almost is not close enough.
The number can only be completely and accurately be represented by 0.9 followed by an infinite amount of 9s. which is not completely 1.
There you go, thats the cave man flaw in our math system.Quote:
Originally Posted by yasunobu13
Three thirds have to equal 1!
No i was only saying that is what you are implying.Quote:
Originally Posted by yasunobu13
Not "can" swap, "have too" swap.Quote:
Originally Posted by yasunobu13
No,Quote:
Originally Posted by yasunobu13
1 represents 1 whole item.
0.999... represents almost 1 whole item.
In these two comments you seem to be contradicting yourself,
Which is it? do you think 0.999... exists or not?Quote:
Originally Posted by yasunobu13
Again no,Quote:
Originally Posted by yasunobu13
The only thing i have seen proof of is the fact that three thirds of one equals one.