Does 0.9999999 = 1?

[Might Tested]

I'm no mathematician but when it comes to this argument i've always thought it was a terrible thing.

A number that is not yet a defined number being compared to a concrete number is just weird.

I may have a misunderstanding seeing as how i didn't study math to this extent, but what would credentials change about absolute values of a number?

When math takes a theoretical turn like this it reminds me of god arguments all over again.

What would make god real to an athiest? The shift from concept to reality would it not?

is a never ending number considered a concrete number? is it really a defined number? If so why would it be considered one?

J, how about you just do what people typically do when they don't understand something. Trust the people who have been studying this extensively.

Luckily, in the world of mathematics, no philosophical nonsense needs to come into play. Mathematicians have defined the rules of real numbers. In this instance, to say .9 repeating is not 1 because .9 repeating is a fictitious concept as opposed to 1 being a real number, is on the same level as saying 1/3 is a fictitious concept. A slim margin of mathematicians deny that 1/3 is .3 repeating. A kid could sit and keep dividing 1 by 3 if he lived forever or prove the result by induction (which is an accepted method of mathematical proofs).

.9 repeating has never ending digits, but its value is not never ending. This is the same as saying 1.000000000.... repeating is not a real number because it has never ending digits, but clearly its value is finite. Thus, it should be fairly intuitive to apply that to .9 repeating. You would be correct however, in stating that a value with never ending magnitude is not a real number. This is why infinity is not a real number. You can't explicitly state infinity's magnitude. Pi is a real number, 3.14159265... is pi's irrational representation, just as .9 repeating is 1's irrational representation.

If you want a "real" way of demonstrating that .9 repeating is 1. Imagine you're on a 1 mile racetrack. You know that you have not reached the finish line if there is a quantifiable distance between your current position and the finish line. For example, if you've driven a quarter mile, then there is still the half mile marker in between you and the finish line. Suppose, you are now .75 of the mile. Well, there's still the .8 mark before you hit the 1 mile line. Now, this will continue until you hit say, .99 , at which point some idiot will say "Ha, we're there", to which you would reply "Well, no, there's still the .995 marker we haven't crossed to get to 1." You could keep incrementing forward to say .9999, but there would still be .999995 that you would have to reach, and that is a quantifiable position between you and the 1 mile marker. Now let's say, you are at .9 repeating. Some ignorant rube will at this point say "Oh, you haven't crossed over to the 1 mile marker, because there's .999999999999....99995 in between you and the 1 mile marker!" But .9 repeating does not end. There is no possible number in between a decimal point and infinite 9s and the number 1, thus you can conclude that the two positions are identical. This may seem a bit absurd, but it's actually a common method of identifying limits using the squeeze theorem. You can google the squeeze theorem if you want, it would probably explain this concept better.

That being said, if you want to completely refute this statement, you would pretty much be flying in the face of calculus and Ph.D mathematicians over centuries, but since it is possible that the majority of the learned community is wrong since the advent of mathematics and the scientific method, state your case in a peer reviewed journal, and proceed to collect an absurd amount of money, fame, and titles.

 

[NYCj360]

Has layeth the smacketh down.

point taken

 

[Scoot Magee]

Lets just say it's almost 1, even if it's off by the smallest fraction it doesn't equal 1.

 

[aj1701]

Lets just say it's almost 1, even if it's off by the smallest fraction it doesn't equal 1.

But that's just not true.

 

[Scoot Magee]

But that's just not true.

Really? So .9999999 does equal 1?

Nevermind lol. I read the above post.

 

[Might Tested]

For anyone reading this now, most of us are making the assumption that Claude meant to write .9 repeating or .(9) or infinite 9s etc.
Obviously .999999999 is just a number close to 1.

 

[Prinz]

J, how about you just do what people typically do when they don't understand something. Trust the people who have been studying this extensively.

Luckily, in the world of mathematics, no philosophical nonsense needs to come into play. Mathematicians have defined the rules of real numbers. In this instance, to say .9 repeating is not 1 because .9 repeating is a fictitious concept as opposed to 1 being a real number, is on the same level as saying 1/3 is a fictitious concept. A slim margin of mathematicians deny that 1/3 is .3 repeating. A kid could sit and keep dividing 1 by 3 if he lived forever or prove the result by induction (which is an accepted method of mathematical proofs).

.9 repeating has never ending digits, but its value is not never ending. This is the same as saying 1.000000000.... repeating is not a real number because it has never ending digits, but clearly its value is finite. Thus, it should be fairly intuitive to apply that to .9 repeating. You would be correct however, in stating that a value with never ending magnitude is not a real number. This is why infinity is not a real number. You can't explicitly state infinity's magnitude. Pi is a real number, 3.14159265... is pi's irrational representation, just as .9 repeating is 1's irrational representation.

If you want a "real" way of demonstrating that .9 repeating is 1. Imagine you're on a 1 mile racetrack. You know that you have not reached the finish line if there is a quantifiable distance between your current position and the finish line. For example, if you've driven a quarter mile, then there is still the half mile marker in between you and the finish line. Suppose, you are now .75 of the mile. Well, there's still the .8 mark before you hit the 1 mile line. Now, this will continue until you hit say, .99 , at which point some idiot will say "Ha, we're there", to which you would reply "Well, no, there's still the .995 marker we haven't crossed to get to 1." You could keep incrementing forward to say .9999, but there would still be .999995 that you would have to reach, and that is a quantifiable position between you and the 1 mile marker. Now let's say, you are at .9 repeating. Some ignorant rube will at this point say "Oh, you haven't crossed over to the 1 mile marker, because there's .999999999999....99995 in between you and the 1 mile marker!" But .9 repeating does not end. There is no possible number in between a decimal point and infinite 9s and the number 1, thus you can conclude that the two positions are identical. This may seem a bit absurd, but it's actually a common method of identifying limits using the squeeze theorem. You can google the squeeze theorem if you want, it would probably explain this concept better.

That being said, if you want to completely refute this statement, you would pretty much be flying in the face of calculus and Ph.D mathematicians over centuries, but since it is possible that the majority of the learned community is wrong since the advent of mathematics and the scientific method, state your case in a peer reviewed journal, and proceed to collect an absurd amount of money, fame, and titles.

1. Saying that mathematics works on a set of made up rules already makes it not representing the reality.
2. o is a symbol that represents nothing, it has no value. So you can add as many zeroes as you like after a comma and they will change absolutely nothing. This is why 0's are not written, because they don't change anything. 1 eill equal 1,0 with any amount of zeroes.
3. About crossing the mile is absolute non-sense. You have that video showing how dividing a distinct distance into halves will never get you to that distance's end because you'll never stop dividing in halves. Xenon said: "Achiles will never outrun a turtle" then he explained "because IF every time the turtle makes a step Achiles will approach by half the distance, so he will always be moving in halves and never reach the turtle". Which is also a rule he made up to fuck with people's mind.
Again, this is an error. 1 does not equal 0.(9) because it's exactly like you're saying with the mile example. Even if it's infinitely close it's also infinitely uneven.
It's just a mindfuck. It doesn't mean anything. Just means the math is not a perfect, absolute thing.

 

[Zoidberg747]

1. Saying that mathematics works on a set of made up rules already makes it not representing the reality.
2. o is a symbol that represents nothing, it has no value. So you can add as many zeroes as you like after a comma and they will change absolutely nothing. This is why 0's are not written, because they don't change anything. 1 eill equal 1,0 with any amount of zeroes.
3. About crossing the mile is absolute non-sense. You have that video showing how dividing a distinct distance into halves will never get you to that distance's end because you'll never stop dividing in halves. Xenon said: "Achiles will never outrun a turtle" then he explained "because IF every time the turtle makes a step Achiles will approach by half the distance, so he will always be moving in halves and never reach the turtle". Which is also a rule he made up to fuck with people's mind.
Again, this is an error. 1 does not equal 0.(9) because it's exactly like you're saying with the mile example. Even if it's infinitely close it's also infinitely uneven.
It's just a mindfuck. It doesn't mean anything. Just means the math is not a perfect, absolute thing.

Number 2 is completely false. The difference between 1 and 1,000,000 dollars is quite meaningful I would say.

 

[Prinz]

Number 2 is completely false. The difference between 1 and 1,000,000 dollars is quite meaningful I would say.

It's 1.00000 for Americans

 

[aj1701]

1. Saying that mathematics works on a set of made up rules already makes it not representing the reality.
2. o is a symbol that represents nothing, it has no value. So you can add as many zeroes as you like after a comma and they will change absolutely nothing. This is why 0's are not written, because they don't change anything. 1 eill equal 1,0 with any amount of zeroes.
3. About crossing the mile is absolute non-sense. You have that video showing how dividing a distinct distance into halves will never get you to that distance's end because you'll never stop dividing in halves. Xenon said: "Achiles will never outrun a turtle" then he explained "because IF every time the turtle makes a step Achiles will approach by half the distance, so he will always be moving in halves and never reach the turtle". Which is also a rule he made up to fuck with people's mind.
Again, this is an error. 1 does not equal 0.(9) because it's exactly like you're saying with the mile example. Even if it's infinitely close it's also infinitely uneven.
It's just a mindfuck. It doesn't mean anything. Just means the math is not a perfect, absolute thing.

ugh. The proof is all around you. We've sent men to the moon, have probes travelling billions of miles to meet up with the outer planets as they move (and we move) and leave our solar system.

The math you dismiss is what Einstein built general relatively on; his equations correctly predict things we now believe to exist like black holes (but some of the terms of his equations have to go to infinity to do so).

Listen, its fine to say you don't understand or can wrap your head around it. People devote their entire lives to understanding this shit. But to dismiss it as "made up rules" just because YOU can't understand it, even though we've used it to advance our civilization leaps and bounds in the past 200 years, that's just absolutely ridiculous.

 

[Prinz]

ugh. The proof is all around you. We've sent men to the moon, have probes travelling billions of miles to meet up with the outer planets as they move (and we move) and leave our solar system.

The math you dismiss is what Einstein built general relatively on; his equations correctly predict things we now believe to exist like black holes (but some of the terms of his equations have to go to infinity to do so).

Listen, its fine to say you don't understand or can wrap your head around it. People devote their entire lives to understanding this shit. But to dismiss it as "made up rules" just because YOU can't understand it, even though we've used it to advance our civilization leaps and bounds in the past 200 years, that's just absolutely ridiculous.

I'm not dismissing anything. I'm just saying this particular problem is not yet entirely solved.

 

[Prinz]

Btw, how do you prove the reversed situation: 0,(9)=1?

 

[Flagg]

Omg you might as well ask what came first, the chicken or the egg, but who cares? So much energy being expended on a debate that will literally have no impact or effect on anyone's life.

 

[Prinz]

Omg you might as well ask what came first, the chicken or the egg, but who cares? So much energy being expended on a debate that will literally have no impact or effect on anyone's life.

Apparently it has

 

[StevoSuprem0]

Sig figs bitch.

 

[EnergyKD]

Test Your Math

 

[Illmatix]

It will never be one, you see .9 is only .1 from becoming 1 and all your doing is infinitely adding up toward that .1 with infinitely smaller numbers that are decreasing so exponentially in value that .1 is never acheived.

 

[Illmatix]

Here's an easier way to showcase what you've done that defies all logic.

1/9 = 0.111
2/9 = 0.222
3/9 = 0.333
..
..
..
8/9 = 0.888

So what's 9/9?

That's awesome this very interesting

 

[Cossner]

 

[Pan1cMode]

I'm not dismissing anything. I'm just saying this particular problem is not yet entirely solved.

No, this 'problem' has long since been solved. The fact that you can't wrap your head around the answer is another thing entirely.

To @Prinz I don't think you've understood the squeeze theorem explanation so I'll go over it again. Basically it states that two numbers are the same number if there are no numbers in between them. 1 and 1.000000000... Do not have any numbers in between them so they are the same number. Likewise, there are no numbers in between 0.9999999... and 1; hence they are the same number.

It will never be one, you see .9 is only .1 from becoming 1 and all your doing is infinitely adding up toward that .1 with infinitely smaller numbers that are decreasing so exponentially in value that .1 is never acheived.

Yes it is 1. There are plenty of explanations as to why in this thread. An infinite number of 9s following a decimal point is the same as 1.

This is the simplest algebraic proof;

1/3 + 1/3 + 1/3 = 0.33333... + 0.33333... +0.33333... = 0.99999... = 1

 

[Prinz]

No, this 'problem' has long since been solved. The fact that you can't wrap your head around the answer is another thing entirely.

To @Prinz I don't think you've understood the squeeze theorem explanation so I'll go over it again. Basically it states that two numbers are the same number if there are no numbers in between them. 1 and 1.000000000... Do not have any numbers in between them so they are the same number. Likewise, there are no numbers in between 0.9999999... and 1; hence they are the same number.


Yes it is 1. There are plenty of explanations as to why in this thread. An infinite number of 9s following a decimal point is the same as 1.

This is the simplest algebraic proof;

1/3 + 1/3 + 1/3 = 0.33333... + 0.33333... +0.33333... = 0.99999... = 1

I understand and I disagree. There's 0,(0)1 between 1 and 0,(9). So they don't equal.

 

[Pan1cMode]

I understand and I disagree. There's 0,(0)1 between 1 and 0,(9). So they don't equal.

That's fine, but you're wrong. It's infinite, tell me the number; write it down. It's not possible because I think you're not grasping the concept of infinite. It's not just a shittonne of 9s, it's forever 9s. There is no end to the sequence so there will never ever be any number between it and 1. It is not some infinitesimally small fraction off from 1, it is equal to 1.

It's good to see that you understand better than hundreds of years of mathematicians who have devoted their lives studying this stuff.

 

[Prinz]

That's fine, but you're wrong. It's infinite, tell me the number; write it down. It's not possible because I think you're not grasping the concept of infinite. It's not just a shittonne of 9s, it's forever 9s. There is no end to the sequence so there will never ever be any number between it and 1. It is not some infinitesimally small fraction off from 1, it is equal to 1.

It's good to see that you understand better than hundreds of years of mathematicians who have devoted their lives studying this stuff.

0,(0)1 also has infinite 0's, but it doesn't mean it equals 0.

 

[Pan1cMode]

0,(0)1 also has infinite 0's, but it doesn't mean it equals 0.
Thank you for the compliment, sir.

If it has infinite zeros, it can't end in a 1. In fact, it literally can't end. There will never be a point at which you can say, "oh now comes the 1".

 

[Akae47]

I am shocked at some of these answer here. 0.99999.... is not 1 and it never will be. In terms of money I'm a accountant I can make .9999 = 1,000,000