The "common sense" proof

[TheSomeone]

-If you keep adding 9 after the decimal point you get closer and closer to 1
-If you add a static infinite amount of 9s it is no longer possible to add anymore 9s and get any closer to 1, because there is no end to infinity, no end to which you can add 9.
-If you cannot get any closer to 1, that means there is NOTHING between that number and 1 (if there was something there then you could get closer by traveling half that distance)
-if there is NOTHING between two numbers, in other words, if their "difference", represented by a minus sign, is zero, they must be the same (1.0000... - 0.999... = 0)

-Logical conclusion, 1 is the same as 0.999...

People who have been denying the math must now accept the truth.

 

[Raziaar]

Lock this thread now. This is just gonna be another spamfest.

 

[bbson john]

Some people will still, senselessly, insist on 0.999... =/= 1 because they just like arguing. It is pointless to continue on this. Though 0.999 = 1 is a well-known fact, people just can't hide their stupidity and ignorance and keep thinking that arguing is so fun, even though no one think it is. That has been enough, close this thread before stupid guys emerge.

 

[63]

What's more interesting is how an Ace can be both 1 and 11!

 

[JellyWorld]

0.99999999999.... = 1.

But your proof is wrong. Never try and use common sense in math

 

[TheSomeone]

0.99999999999.... = 1.

But your proof is wrong. Never try and use common sense in math

I agree with you, but my proof is still correct.
It's not so much a proof as an explanation for people who, after seeing the mathematical proof, sill don't get it.

 

[sinkoman]

I see what you are saying, but I can't agree that it's COMPLETELY equal to one.

More like, it's an alias of one.

Because, logically, a number is itself, and isn't another number. 5 is 5, not 6. 1.3333 is 1.333, not 1.444 or 1.222.

But I get what you are saying.

 

[bbson john]

I see what you are saying, but I can't agree that it's COMPLETELY equal to one.

More like, it's an alias of one.

Because, logically, a number is itself, and isn't another number. 5 is 5, not 6. 1.3333 is 1.333, not 1.444 or 1.222.

But I get what you are saying.

1.999... = 2 and 1.3333... = 1.444... are two different cases. I can tell you the difference between 1.3333... and 1.4444... is 0.1111..... But you cannot tell what is the difference between 1.999... and 2, certainly is not 0.111... If you want to apply the case on different numbers, you can say 1.333...339 = 1.333...340. However, this doesn't exist since we cannot add a number which is infinitively small. Thus, .9999... is a special case.

Time to spam, pals
(Time to lock, mods)

 

[jondy]

Because, logically, a number is itself, and isn't another number. 5 is 5, not 6. 1.3333 is 1.333, not 1.444 or 1.222.

No, the problem only occurs at decimal points. 0.99.. ,1.99.. , etc.

EDIT: nvm, I see what you were getting at

 

[sinkoman]

1.999... = 2 and 1.3333... = 1.444... are two different cases. I can tell you the difference between 1.3333... and 1.4444... is 0.1111..... But you cannot tell what is the difference between 1.999... and 2, certainly is not 0.111... If you want to apply the case on different numbers, you can say 1.333...339 = 1.333...340. However, this doesn't exist since we cannot add a number which is infinitively small. Thus, .9999... is a special case.

Time to spam, pals
(Time to lock, mods)

Well, I was trying to say, a number is itself, not another number.

5 is 5, not 4.

Although I agree with your argumen, 1.9 repeating is an ALIAS of 1, but I will not accept that it IS 1.

1 is one. 2 isn't one, 2 is too. .5 isn't one, .5 is .5.

Numbers are NEVER another number. But in this case, they "may as well be".

 

[JellyWorld]

A number can never equal a different number.
A decimal however, can equal another distindt decimal.

 

[sinkoman]

A number can never equal a different number.
A decimal however, can equal another distindt decimal.

Touche' :O

 

[RakuraiTenjin]

.9999... goes on forever with 9's, it never reaches one. You can only get to 1 by rounding.

It continues on with 9's forever. Forever and ever, for eons and never stops- it never reaches one.

 

[bbson john]

Well, I was trying to say, a number is itself, not another number.

5 is 5, not 4.

Although I agree with your argumen, 1.9 repeating is an ALIAS of 1, but I will not accept that it IS 1.

1 is one. 2 isn't one, 2 is too. .5 isn't one, .5 is .5.

Numbers are NEVER another number. But in this case, they "may as well be".

So is 1 = 2/2? Is 4 = root2? 1 = log10?
Numbers are always themselves, you're right. They just wear different clothes. In this case, 2 wore a wired one, i.e. 1.999....

 

[Teta_Bonita]

As 0.999... repeating becomes more precise, it approaches 1 as a limit. When 0.999... has infinite presicion it can be treated as 1, but it does not nessessarily equal 1.

 

[jondy]

.9999... goes on forever with 9's, it never reaches one. You can only get to 1 by rounding.

It continues on with 9's forever. Forever and ever, for eons and never stops- it never reaches one.

LOL @ Rakurai not knowing math

 

[bbson john]

.9999... goes on forever with 9's, it never reaches one. You can only get to 1 by rounding.

It continues on with 9's forever. Forever and ever, for eons and never stops- it never reaches one.

GOOD POINT! 'cos it goes forever, so it IS EQUAL 1. Tell me, what is 1 - 0.999...?

 

[_Z_Ryuken]

GOOD POINT! 'cos it goes forever, so it IS EQUAL 1. Tell me, what is 1 - 0.999...?

0.001

 

[Ludah]

1 =/= 2

1 =/= 5

1 =/= 12

1 =/= 0.5

1 =/= 0.67

1 =/= 120

1 =/= 0.9999...

1 = 1

One will always be one. There will never be another number that can also be one. It's really simple. You can say 0.9999 is equal to one out of convenience, if you want. But you need to admit that it's still flawed.

 

[sinkoman]

1 =/= 2

1 =/= 5

1 =/= 12

1 =/= 0.5

1 =/= 0.67

1 =/= 120

1 =/= 0.9999...

1 = 1

One will always be one. There will never be another number that can also be one. It's really simple.

Exactly.

BUT, what these guys are trying to say, is that .9 repeating may as well be 1

0.001

 

[Ludah]

"May as well" is a convenience. And I agree. In the nitty gritty though, they are distinct from each other.

 

[jondy]

"May as well" is a convenience. And I agree. In the nitty gritty though, they are distinct from each other.

When you say 'distinct', what do you mean? The only thing that separates them is the way that they're written... 0.99... has the exact same numerical value as one. So any 'distinction' is an arbitrary issue of representation

 

[_Z_Ryuken]

Where do you draw the line? When is 0.99 repeating no longer a fraction?

 

[jondy]

Where do you draw the line? When is 0.99 repeating no longer a fraction?

It never is a fraction, 0.9 recurring can't be expressed as a fraction other than 1/1, 3/3 etc because it =1.

0.9 recurring is a fixed value, it doesn't 'approach' anything

 

[15357]

0.999999999....... =1

Its a goddamned fraction that you learn about in 4th grade.

 

[Murray]

Umm, 0.999... != 1, because no matter how many nines you add to the decimal, you'll never reach 1. Infinity has no end to it. You can't just add infinite 9's and expect that you're at your limit. THERE IS NO LIMIT!
Infinity is an ungraspable number, you can't use that as an excuse that the number has nothing between it. There is always another decimal step you can add.

 

[RakuraiTenjin]

1 =/= 2

1 =/= 5

1 =/= 12

1 =/= 0.5

1 =/= 0.67

1 =/= 120

1 =/= 0.9999...

1 = 1

One will always be one. There will never be another number that can also be one. It's really simple. You can say 0.9999 is equal to one out of convenience, if you want. But you need to admit that it's still flawed.

QFTMFT!!!!

I've been saying this in every single thread about this but people just try to shout down common sense.

Like someone else said, it approaches one forever but it never ever will reach it.

 

[15357]

Please note that if 0.99999... was not 1, a lot of the fundamentals of math and arithmancy would be rendered null and void.

 

[Ludah]

When you say 'distinct', what do you mean? The only thing that separates them is the way that they're written... 0.99... has the exact same numerical value as one. So any 'distinction' is an arbitrary issue of representation

No, it has a numerical value constantly approaching 1, but will never reach it. It simply goes on for infinity.

 

[RakuraiTenjin]

Please note that if 0.99999... was not 0, a lot of the fundamentals of math and arithmancy would be rendered null and void.

Assuming you mean 1. It may as well be 1 rounding wise and in practical use, but it isn't by definition. It never reaches the integer one.

 

[15357]

If it wasn't 1, it could be made into a fraction that didn't divide into 1.

 

[jondy]

Umm, 0.999... != 1, because no matter how many nines you add to the decimal, you'll never reach 1. Infinity has no end to it. You can't just add infinite 9's and expect that you're at your limit. THERE IS NO LIMIT!
Infinity is an ungraspable number, you can't use that as an excuse that the number has nothing between it. There is always another decimal step you can add.

I've been saying this in every single thread about this but people just try to shout down common sense.

Like someone else said, it approaches one forever but it never ever will reach it.

Maths has NOTHING whatsoever to do with common sense and intuition. Cast aside anything you 'think' you know... until you've proved you're correct, you don't have a case.

0.9 recurring doesn't 'approach' anything, it's a fixed value. You can't keep 'adding nines' in the same way that it's pointless to keep adding noughts to 0.

0.9, 0.99, 0.999 is a sequence that approaches 0.9 recurring (and hence 1) but 0.9 recurring itself is a fixed value

 

[_Z_Ryuken]

It never is a fraction, 0.9 recurring can't be expressed as a fraction other than 1/1, 3/3 etc because it =1.

0.9 recurring is a fixed value, it doesn't 'approach' anything

9/10
99/100
999/1000
9999/1000
99999/10000

What are you talking about?

 

[Stingey]

I suggest we employ the empirical approach, as in write down as many decimals as possible and wait until it turns into a 1. Cya soon, probably when i run out of paper.

 

[jondy]

No, it has a numerical value constantly approaching 1, but will never reach it. It simply goes on for infinity.

You're incorrect, it doesn't 'approach' anything. Numbers can't approach anything, by their nature they are constant. Does 0.3 recurring approach 1/3? No, because it is 1/3

 

[RakuraiTenjin]

Maths has NOTHING whatsoever to do with common sense and intuition. Cast aside anything you 'think' you know... until you've proved you're correct, you don't have a case.

0.9 recurring doesn't 'approach' anything, it's a fixed value. You can't keep 'adding nines' in the same way that it's pointless to keep adding noughts to 0.

0.9, 0.99, 0.999 is a sequence that approaches 0.9 recurring (and hence 1) but 0.9 recurring itself is a fixed value

.9999... infinite 9's. IT NEVER REACHES ONE. IT JUST GOES ON WITH NINES FOREVER AND EVER.

 

[jondy]

9/10
99/100
999/1000
9999/1000
99999/10000

What are you talking about?

What you're saying is that 0.99..../1 = 0.9...

none of those fractions hit 0.9recurring... the sequence you describe will approach it, but won't ever equal it

.9999... infinite 9's. IT NEVER REACHES ONE. IT JUST GOES ON WITH NINES FOREVER AND EVER.

hehe, until you study maths Rakurai stay the hell away , I can prove my result and you can't, and that's what matters

 

[bliink]

Look, 0.9 recurring is a number. Let a number = x

0.99999... = x
1 = x
0.9 = x
1.888.... = x
2 = x

etc

Therefore, 0.9999... equals x, and as stated, x = 1. It also equals 0.9999.... and 1.88888... and 2 and 4 and 42 and 66 and 5934.

Therefore, they all equal the same thing, and cancel each other out.
Therefore, maths does not exist.

Therefore, you are all noobs.

 

[jondy]

Therefore, you are all noobs.

BUT THE NINES CARRY ON FOREVER!1

 

[Murray]

Look, 0.9 recurring is a number. Let a number = x

0.99999... = x
1 = x
0.9 = x
1.888.... = x
2 = x

etc

Therefore, 0.9999... equals x, and as stated, x = 1. It also equals 0.9999.... and 1.88888... and 2 and 4 and 42 and 66 and 5934.

Therefore, they all equal the same thing, and cancel each other out.
Therefore, maths does not exist.

Therefore, you are all noobs.

Yes, I guess you're right.
I was a fool to belive otherwise. Thank you for making my life easier.