1 = .999?

[LukaP]

what..? 9*0.09999 is not 9 and it's definitely not 9*1

no its not. lets go over it slower

 

0.9999*10 = 9.9999999 (all of this periodic) simple multiplication, alls good here right?

9.9999-0.9999 ive taken the result from above, and subtracted the original number = 9 this simple subtraction gives us this result, alls good right? = so then as we agree that we have subtracted one of the 10 factors in the original multiplication, we can also say (10-1) or as its more commonly known 9*0.9999 = and as the last two expressions are equal 9*1  ergo

0.9999 = 1

[Arty]

Take Calculus.

It helps 

 

1 does = .9999 etc

and

 1.0000reapting 1

[LukaP]

it's still not actually equaling one

it is. because it goes to infinity. imagine a function of 1/x. its limit is 0. does it reach 0 ever. of course no, not until infinity. but its limit there is 0, ergo its lowest point is 0. this is analagous just that its a series of 1/10ⁿ being summed together. the sum never reacher 1, but it limits to 1, so it must equal that at infinity

[ZetZet]

yes, 1 = 0.9 recurring. It's perfectly provable.

1/9 = 0.1 recurring.

1/9*9 = 1.

0.1recurring*9 = 0.9recurring = 1.

Those who deny it don't understand math.

it's provable by math, but it doesn't make logical sense like 1/3 recurring does so it's an argument of discussion. what's there to deny.

 

it is. because it goes to infinity. imagine a function of 1/x. its limit is 0. does it reach 0 ever. of course no, not until infinity. but its limit there is 0, ergo its lowest point is 0. this is analagous just that its a series of 1/10ⁿ being summed together. the sum never reacher 1, but it limits to 1, so it must equal that at infinity

the point of limit is that you can never reach it, it never gets there, that's why you don't type = 0 it can't equal that at infinity because there is no such thing as infinity in the world we live in. 

 

Like I said, it makes sense in math, it doesn't make nearly as much sense in life like 1/3 or 2/3 does.

[Sauron]

it's provable by math, but it doesn't make logical sense like 1/3 recurring does so it's an argument of discussion. what's there to deny.

 

 

the point of limit is that you can never reach it, it never gets there, that's why you don't type = 0

 

Uh what? It makes perfect sense. 1/9*9=1 by definition. Math is nothing but logic applied to a a small set of preset rules.

Here is the wikipedia page that contains both the "easy" intuitive proof that I showed, plus the completely undenyable analytic ones.

https://en.wikipedia.org/wiki/0.999...

[ZetZet]

Uh what? It makes perfect sense. 1/9*9=1 by definition. Math is nothing but logic applied to a a small set of preset rules.

Here is the wikipedia page that contains both the "easy" intuitive proof that I showed, plus the completely undenyable analytic ones.

https://en.wikipedia.org/wiki/0.999...

yes. 1/9 makes sense. 9999999999999999999999999999999999999999999999999999999*/1000000000000000000000000000000000000000000000000000000000000000* does not.

[LukaP]

it's provable by math, but it doesn't make logical sense like 1/3 recurring does so it's an argument of discussion. what's there to deny.

 

 

the point of limit is that you can never reach it, it never gets there, that's why you don't type = 0 it can't equal that at infinity because there is no such thing as infinity in the world we live in. 

 

Like I said, it makes sense in math, it doesn't make nearly as much sense in life like 1/3 or 2/3 does.

its just a way of typing it ffs. a decimal notation. we have 3 (actually 4) ways to type an integer in decimal. 0.9999999, 1, 1.000000000 and 1.00000(recurring)0000001. they all hold the same value, its a downside of the decimal notation. it makes sense.

and no, the point of limit is not that you never reach it, the point of it is it describes how a function/series behaves for big n. and that is exactly what we care about. what does this do if n rises through the roof. (also, you do type lim(expression) = number, so there)

[Sauron]

yes. 1/9 makes sense. 9999999999999999999999999999999999999999999999999999999*/1000000000000000000000000000000000000000000000000000000000000000* does not.

 

except this

 

 

 

9999999999999999999999999999999999999999999999999999999*/1000000000000000000000000000000000000000000000000000000000000000*

 

is not 0.9* because you can't define the power of 10. Whereas you can define exactly what 0.9* is - it's 1/9*9. Which is also 1.

 

I don't understand why seeing a number in two different forms bothers you so much. Do you have a problem with 1=-e^iπ too?

[KemoKa]

Wow, I thought I would never live to see the day when a raging flame war would be wrought over such a fundamental absolute as mathematics. Politics, philosophy, religion, history, sure, happens a thousand times a day!!

 

But MATH?!

 

I guess I was wrong.

[LukaP]

except this

 

 

is not 0.9* because you can't define the power of 10. Whereas you can define exactly what 0.9* is - it's 1/9*9. Which is also 1.

 

I don't understand why seeing a number in two different forms bothers you so much. Do you have a problem with 1=-e^iπ too?

or e being defined by a limit as well. lim(1+1/x)^x = e. its the exact same thing, just a different series/function

[ZetZet]

I don't understand why seeing a number in two different forms bothers you so much.

it doesn't. what bothers me is that by definition 0.9* can never actually reach 1 in logical sense.

 

1-0.9* still has something left over.

 

 

i get that it's proven by math and such. But as we know math isn't all powerful, we don't even know what pi is in the first place.

[LukaP]

it doesn't. what bothers me is that by definition 0.9* can never actually reach 1 in logical sense.

 

1-0.9* still has something left over.

no it does not. -.- have you even seen my mathematical, as well as philisophical proof? if you want i can prove it to you with a limit as well. (also if you dont believe me about limits, i suggest you read on them)

[Sauron]

it doesn't. what bothers me is that by definition 0.9* can never actually reach 1 in logical sense.

 

1-0.9* still has something left over.

 

All right, tell me what 1-0.9* is then.

 

And read up what "by definition" means.

[ZetZet]

All right, tell me what 1-0.9* is then.

 

And read up what "by definition" means.

I can't tell you what 4-pi is either, does that mean there isn't something left over? does pi = 4?

[LukaP]

I can't tell you what 4-pi is either, does that mean there isn't something left over? does pi = 4?

i can tell you exactly what 4pi is. its 4 times the ratio of diameter and circumference (or there about not sure if its defined with diameter or radius) of a circle.

 

I can also tell you exactly what 1-0.9999999999 is. its 0.00000000000(reccuring)00001, where 1 is the absolute last digit. but as we know, decimal numbers do not have a last digit in their notation, ergo that is impossible, and you never come to that 1. meaning the solution is actually 0.0000000* which we also shorten into 0

[ZetZet]

i can tell you exactly what 4pi is. its 4 times the ratio of diameter and circumference (or there about not sure if its defined with diameter or radius) of a circle.

 

I can also tell you exactly what 1-0.9999999999 is. its 0.00000000000(reccuring)00001, where 1 is the absolute last digit. but as we know, decimal numbers do not have a last digit in their notation, ergo that is impossible, and you never come to that 1. meaning the solution is actually 0.0000000* which we also shorten into 0

i said 4        -        pi

[Sauron]

I can't tell you what 4-pi is either, does that mean there isn't something left over? does pi = 4?

 

Weird, because I (and anyone who can use a calculator) can tell you what 4-pi is with a reasonable approximation. It's about 0.8584073464102067615373566167205. Not only that, following the previous formula, 4-pi=4-log(-1)/i.

Now, give me an approximation of 1-0.9* to any order you wish, or any equation that defines it.

[ZetZet]

Weird, because I (and anyone who can use a calculator) can tell you what 4-pi is with a reasonable approximation. It's about 0.8584073464102067615373566167205. Not only that, following the previous formula, 4-pi=4-log(-1)/i.

Now, give me an approximation of 1-0.9* to any order you wish, or any equation that defines it.

there we go again, we approximate, we assume. But you can never say that it is that number or it isn't.

[LukaP]

i said 4        -        pi

same shit, just a different expression, as apart from defining pi, its all simple algebra

there we go again, we approximate, we assume. But you can never say that it is that number or it isn't.

yes, now i ask you to even with approximation to any degree, (ergo limiting towards infinity) show that 1-0.9* is anything but 0. if you do i will reference you in my paper, as i go pick my PhD and any awards i may get.

[Sauron]

there we go again, we approximate, we assume. But you can never say that it is that number or it isn't.

 

Approximation is a way to allow people to write infinite numbers. If the only proof you'll take for defining a number is working it out and physically see it written down to the end, you do not understand how math works.

 

We showed you multiple ways to prove that 0.9* IS 1. If you want to continue insisting on a point that was proven wrong multiple times and refuse any logical proof we put before you, be my guest. It's like talking to a man who insists he is a turtle and says we can't prove he isn't because we can't manually unravel his dna to show him the differences.

[LukaP]

Approximation is a way to allow people to write infinite numbers. If the only proof you'll take for defining a number is working it out and physically see it written down to the end, you do not understand how math works.

 

We showed you multiple ways to prove that 0.9* IS 1. If you want to continue insisting on a point that was proven wrong multiple times and refuse any logical proof we put before you, be my guest. It's like talking to a man who insists he is a turtle and says we can't prove he isn't because we can't manually unravel his dna to show him the differences.

except one could manually look at the molecule of his and a turtles DNA under a SEM, but one can never (actually by definition) write down any number in decimal notation without approximation or some sort of a standard (ommiting the leading and trailing 0s is one of them)

[Sauron]

except one could manually look at the molecule of his and a turtles DNA under a SEM, but one can never (actually by definition) write down any number in decimal notation without approximation or some sort of a standard (ommiting the leading and trailing 0s is one of them)

 

you can write down 0.9* using the tools provided by math, namely the dot on top of the 9 or simply 1/9*9. Right now, it's as if he was calling bs on the microscope and saying we can't prove what we're actually seeing is his dna.

[LukaP]

you can write down 0.9* using the tools provided by math, namely the dot on top of the 9 or simply 1/9*9. Right now, it's as if he was calling bs on the microscope and saying we can't prove what we're actually seeing is his dna.

yes but those are the standards i talked about

 

By definition a decimal number is of this shape

infinite leading zeros, integer whose value is defined through the base10 system, decimal period, a series of numbers, whose value is again described by base10, that may or may not be finite in lenght, *if finite* infinite trailing zeroes.

 

we can omit the leading and trailing zeroes, and we can move the decimal period around as long as we then somehow note how much it has been moved (done usually with a *10ⁿ)

[Sauron]

yes but those are the standards i talked about

 

By definition a decimal number is of this shape

infinite leading zeros, integer whose value is defined through the base10 system, decimal period, a series of numbers, whose value is again described by base10, that may or may not be finite in lenght, *if finite* infinite trailing zeroes.

 

we can omit the leading and trailing zeroes, and we can move the decimal period around as long as we then somehow note how much it has been moved (done usually with a *10ⁿ)

 

Actually I don't think that's a thing either, an infinite number cannot have a "last digit" if you know what I mean. 0.0*1 is not something you can write. 0.9* is simply 1 with no approximation, for the reasons we showed earlier - there is nothing missing in 1/9*9=1, it's 100% true. You'd need to use lim(1*10^x) for x->infinity, which is quite simply 0.

[Arty]

no it does not. -.- have you even seen my mathematical, as well as philisophical proof? if you want i can prove it to you with a limit as well. (also if you dont believe me about limits, i suggest you read on them)

/\

this

 

 

 

@Deniers

Take Calculus, learn math

then come back here and speak.