0.999... = 1 - General - Facepunch Forum

[quote]Also who and why decided to prove something that is no way beneficial to anything everywhere. Just use something that suits you and doesn't bother you during calculations. Round numbers only when you write the result, keep the big numbers you work on to the calculator to remember. Have a nice day.[/QUOTE] That's what mathematicians do. They solve mathematical problems.

[QUOTE=Coffee;35308490]This is why engineering is better, we just round numbers to 3 significant figures and leave it at that.[/QUOTE] It's like math except with the interesting bits and actual thought left out and the tedious calculation left in. [editline]26th March 2012[/editline] [QUOTE=Corey_Faure;35308633]Basics of other side: .9999999999... isn't 1.[/QUOTE] This side is wrong. .999... is not approximately equal to one. It is precisely one.

[QUOTE=JohnnyMo1;35308938]It's like math except with the interesting bits and actual thought left out and the tedious calculation left in. [/QUOTE] Dude...I wouldn't insult an engineer. He might remember this the next time you need a dispenser.

The only issue is adding them. You lose a .->1 every time you add two .999rs together, whereas 1+1 is always exactly 2. Sure, in small amounts (the .999r in question), .999r can be rounded up to 1, but realistically .999r is exactly what it is and nothing more.

[QUOTE=woolio1;35309027]The only issue is adding them. You lose a .->1 every time you add two .999rs together, whereas 1+1 is always exactly 2. Sure, in small amounts (the .999r in question), .999r can be rounded up to 1, but realistically .999r is exactly what it is and nothing more.[/QUOTE] Ok, how much do you lose when you multiply .9... by 2? Give me a number.

[QUOTE=woolio1;35309027]The only issue is adding them. You lose a .->1 every time you add two .999rs together, whereas 1+1 is always exactly 2. Sure, in small amounts (the .999r in question), .999r can be rounded up to 1, but realistically .999r is exactly what it is and nothing more.[/QUOTE] No. As the number of nines goes off to infinity you're "losing" less when you add two of them together the the point where you lose none when you have infinite nines. This is because .999... = 1. This is mathematical fact, people. Not a question of rounding or anything.

I mean, 0.9 * 2 = 1.8. By your logic 0.9... * 2 should be 0.9...8. What place is the 8 in? How many 9s are there before you get to an 8?

Actually, the existence of the 8 depends on there not being a 9 after it. Which is not true for an infinite series of 9's

[QUOTE=yawmwen;35309134]I mean, 0.9 * 2 = 1.8. By your logic 0.9... * 2 should be 0.9...8. What place is the 8 in? How many 9s are there before you get to an 8?[/QUOTE] Infinite numbers are unfeasible and irrelevant after a certain point. They're also hell to use accurately, although they themselves are infinitely accurate. Why can't we just go as far as necessary, then round off the last digit, as is normal and customary?

[QUOTE=woolio1;35309177]Infinite numbers are unfeasible and irrelevant after a certain point. They're also hell to use accurately, although they themselves are infinitely accurate. Why can't we just go as far as necessary, then round off the last digit, as is normal and customary?[/QUOTE] No, I want to hear you answer this. What place is the 8 in? It [I]has[/I] to be somewhere if you are correct. If there isn't an 8, and 0.9... * 2 = 1.9... then that means that 1.9... = 2, using the other mathematical proofs above.

[QUOTE=woolio1;35309177]Infinite numbers are unfeasible and irrelevant after a certain point. They're also hell to use accurately, although they themselves are infinitely accurate. Why can't we just go as far as necessary, then round off the last digit, as is normal and customary?[/QUOTE] Because mathematicians are after truth, not approximation. And as long as your definitions and language are precise, there is no difficulty in working with them. This is the purpose of analysis. Also, while approximation may be all well and good for engineers, even if you're doing an application of mathematics with a sufficient level of abstraction approximation may not cut it. My general relativity class, for example. It's not pure mathematics but if you're trying to prove relevant facts about the geometry of spacetime "close to true" just isn't enough.

[QUOTE=yawmwen;35309199]No, I want to hear you answer this. What place is the 8 in? It [I]has[/I] to be somewhere if you are correct. If there isn't an 8, and 0.9... * 2 = 1.9... then that means that 1.9... = 2, using the other mathematical proofs above.[/QUOTE] It's at the end of the infinite. Since we can't count to the infinite, it's wedged in there wherever you declare the end to be. This really is more a logic question than a mathematical one, isn't it?

[QUOTE=woolio1;35309268]It's at the end of the infinite. Since we can't count to the infinite, it's wedged in there wherever you declare the end to be. This really is more a logic question than a mathematical one, isn't it?[/QUOTE] To declare there to be an end to something infinite is a contradiction. Also, mathematics is just a manifestation of formal logic.

[QUOTE=woolio1;35309268]It's at the end of the infinite. Since we can't count to the infinite, it's wedged in there wherever you declare the end to be. This really is more a logic question than a mathematical one, isn't it?[/QUOTE] IT IS INFINITE. THERE IS NO END AND YOU CANNOT DECLARE AN END! Can you say with certainty that there is a number between 2(.9...) and 2?

[QUOTE=woolio1;35309268]It's at the end of the infinite. Since we can't count to the infinite, it's wedged in there wherever you declare the end to be. This really is more a logic question than a mathematical one, isn't it?[/QUOTE] There is no end to an infinite, that's the whole point of infinity. If the 8 is at the end of infinity, and infinity goes on forever, then that means the 8 [I]doesn't exist[/I]. That means that 0.9... * 2 is 1.9..., there will never be an 8 because there will never be an end to the repeating 9. This validates the other mathematical proofs. Logically, if 0.9... is equal to 1, then 0.9... multiplied by any number should end with .9...

is there still seriously a debate about this what is wrong with you guys [QUOTE=woolio1;35309268]It's at the end of the infinite. Since we can't count to the infinite, it's wedged in there wherever you declare the end to be. This really is more a logic question than a mathematical one, isn't it?[/QUOTE] "End of infinite" ahaha wow what a great joke that was funn- oh wait you're serious

[QUOTE=J!NX;35309610]is there still seriously a debate about this what is wrong with you guys "End of infinite" ahaha wow what a great joke that was funn- oh wait you're serious[/QUOTE] That actually was meant to be a joke. I guess not everyone has a sense of humor.

[QUOTE=woolio1;35309702]That actually was meant to be a joke. I guess not everyone has a sense of humor.[/QUOTE] I don't think you have a sense of humor, considering that joke wasn't very well done at all.

How fucking stupid would you have to be to seriously think 0.9 repeating is 1? for fucks sakes

[QUOTE=Phantasy;35309960]How fucking stupid would you have to be to seriously think 0.9 repeating is 1? for fucks sakes[/QUOTE] you should know

[QUOTE=Phantasy;35309960]How fucking stupid would you have to be to seriously think 0.9 repeating is 1? for fucks sakes[/QUOTE] "The opinions that are held with passion are always those for which no good ground exists; indeed the passion is the measure of the holders lack of rational conviction."

[QUOTE=Phantasy;35309960]How fucking stupid would you have to be to seriously think 0.9 repeating is 1? for fucks sakes[/QUOTE] Stupid enough to get an education in math.

[QUOTE=MountainWatcher;35308438]I don't understand your point regarding the circles. Also, do you have anything to say about how the probability of guessing the same specific number in a number line as someone else is 0? I understand statistic accepts this result, but if my chance of picking a certain number is 0, then it's impossible for me to pick any number.[/QUOTE] "Probability zero" and "impossible outcome" are not equivalent things---impossible outcomes is a much stronger idea. That is, ALL impossible outcomes have zero probability of occurring, but just because something has zero probability of occurring does not make it impossible. Your example is fine: The probability of two people choosing the exact same number from the set of natural numbers is 0, but clearly not impossible.

[QUOTE=yawmwen;35310281]Stupid enough to get an education in math.[/QUOTE] The goddamn thing is though, I see you're point, but .9 repeating is definitively equal to .9 repeating, not one. It's common sense.

[QUOTE=Phantasy;35310379]The goddamn thing is though, I see you're point, but .9 repeating is definitively equal to .9 repeating, not one. It's common sense.[/QUOTE] .25 is definitively equal to .25, not 1/4. It's common sense.

For all practical intents and purposes, .999... can indeed be considered one. Whether or not it IS one is a different thing entirely. One is one because it's called one. .999..., then, can never be 1, because we don't call it 1. Calling it 1 would change it to 1, thereby nullifying the repeating decimals entirely. It is both .999... and 1. At the same time. The only difference is how you interpret it. Also, I do apologize for my earlier remarks. They were almost entirely boundless. Now that I've had some time to think about it, there really isn't much of a difference between .999... and 1, aside from the name.

[QUOTE=sealclubber;35310319]"Probability zero" and "impossible outcome" are not equivalent things---impossible outcomes is a much stronger idea. That is, ALL impossible outcomes have zero probability of occurring, but just because something has zero probability of occurring does not make it impossible. Your example is fine: The probability of two people choosing the exact same number from the set of natural numbers is 0, but clearly not impossible.[/QUOTE] I thought he was talking about from the reals but that works too.

[QUOTE=woolio1;35310528]For all practical intents and purposes, .999... can indeed be considered one. Whether or not it IS one is a different thing entirely. One is one because it's called one. .999..., then, can never be 1, because we don't call it 1. Calling it 1 would change it to 1, thereby nullifying the repeating decimals entirely. [/QUOTE] That's basically like saying this: [QUOTE=JohnnyMo1;35310525].25 is definitively equal to .25, not 1/4. It's common sense.[/QUOTE]

[QUOTE=woolio1;35310528]For all practical intents and purposes, .999... can indeed be considered one. Whether or not it IS one is a different thing entirely. One is one because it's called one. .999..., then, can never be 1, because we don't call it 1. Calling it 1 would change it to 1, thereby nullifying the repeating decimals entirely. It is both .999... and 1. At the same time. The only difference is how you interpret it. Also, I do apologize for my earlier remarks. They were almost entirely boundless. Now that I've had some time to think about it, there really isn't much of a difference between .999... and 1, aside from the name.[/QUOTE] I don't see why it's impossible to have two numbers with the same value.

[QUOTE=Phantasy;35310379]The goddamn thing is though, I see you're point, but .9 repeating is definitively equal to .9 repeating, not one. It's common sense.[/QUOTE] .9... is equal to 3/3.