Does 0.9999 equal 1?

[Pee_Wee_Herman]

My opinion is that it doesn't. If one is to be one, then it has to be exactly one. Having 0.9999 is 0.0001 short of 1, which makes perfect sense.

What do you guys think? Is my opinion accurate or am I deep diving into semantics?

 

[Caesar]

0.9999 is not equal to one

0.9999... (recurring) is equal to one

 

[Moonwatcher]

For any difference between 0.99 recurring and 1 you choose there is an n (number of digits) where 0.999...(n times)..9 is within that distance. This is true only for the number 1. Ultimately we have to define what number this recurring expansive represents. It's simpler to choose that number to be 1.

 

[Pee_Wee_Herman]

0.9999 is not equal to one

0.9999... (recurring) is equal to one

You're incorrect.

0.9999... (recurring) is not equal to one regardless of how many nines there are. It's still a tiny point away from being one.

 

[Moonwatcher]

You're incorrect.

0.9999... (recurring) is not equal to one regardless of how many nines there are. It's still a tiny point away from being one.

The value is defined as being the limit of the sequence 0.9 , 0.99, 0.999... It is not defined as being any of those particular numbers.

 

[Caesar]

It's still a tiny point away from being one.

then I am sure you can tell me the value of the difference

 

[Taylor]

You're incorrect.

0.9999... (recurring) is not equal to one regardless of how many nines there are. It's still a tiny point away from being one.

There is a point at whichever unit you are using to measure will become too large for the difference between the 0.99 recurring and one that you are not able to measure it. Even the representation of the figure could use more atoms then there are in the universe on which to scribe it.

Functionally, practically, physically it will be one.

 

[Caesar]

Functionally, practically, physically it will be one.

Not just practically, it is exactly one. There is no space within the real number system between 0.999 recurring and 1, so they are simply different ways of expressing a single identity.

for example

let x = 0.999…

therefore 10x = 9.999…

10x - x = 9.999… - 0.999…

9x = 9

x = 1

qed

 

[Pee_Wee_Herman]

It makes me sad to see people so horribly misinformed.

To clarify, if two numbers have different decimal representations, they must be different numbers. Since 0.9999 and 1 have distinct decimal representations, they would not be equal.

 

[Moonwatcher]

It makes me sad to see people so horribly misinformed.

To clarify, if two numbers have different decimal representations, they must be different numbers. Since 0.9999 and 1 have distinct decimal representations, they would not be equal.

But we are not comparing 0.9999 with 1 we are defining what the limit of the sequence should be.

 

[Moonwatcher]

But I know you don't actually disagree and are just trying to generate conversation. Credit to you sir

 

[Pee_Wee_Herman]

But we are not comparing 0.9999 with 1 we are defining what the limit of the sequence should be.

The point os this thread is to determine if 0.9999 is equal to 1, which it isn't. It's not to define the limit of the sequence.

 

[Moonwatcher]

The point os this thread is to determine if 0.9999 is equal to 1, which it isn't. It's not to define the limit of the sequence.

Well damn, you're right. Sorry to impugn your reputation.

 

[raskolnikov]

 

[Gough]

Depends if you're a coke dealer.

 

[Frank Bunn]

There is a point at whichever unit you are using to measure will become too large for the difference between the 0.99 recurring and one that you are not able to measure it. Even the representation of the figure could use more atoms then there are in the universe on which to scribe it.

Functionally, practically, physically it will be one.

There's a difference between theoretical numbers and the real world. 1 minus 0.999 recurring is infinitesimal. It's the same as 1/∞. It's fun for calculus and thought experiments.

In the real world the difference between 1 and 0.9999 depends on context. F1 races are decided by one thousandth of a second so for that practical purpose 1 and 0.9999 of a second are the same thing. If you were making an atomic clock that same discrepancy would be failure. Same for an astrophysicist doing calculations of 1 light year compared to 0.9999 of that distance.

 

[Pee_Wee_Herman]

View attachment 1768295

"When a true genius appears in the world, you may know him by this sign, that the dunces are all in confederacy against him."

 

[Ace Rimmer]

"When a true genius appears in the world, you may know him by this sign, that the dunces are all in confederacy against him."

I don't know anything about maths, but that's a blooming great book.

 

[Richard Cranium]

"When a true genius appears in the world, you may know him by this sign, that the dunces are all in confederacy against him."

“First they think you're crazy, then they fight you, then you change the world.” - Elizabeth Holmes

 

[Purple7x08_24]

I hope the OP is an engineer