What is .99 repeating as a fraction?
(5x + x) / 6 = x
Sqrt ((2x*3x)/6) = x
When you are proving something, it doesn't have to hold true for all numbers. For instance, I could create a proof to show that pi is an irrational number. I wouldn't expect to be able to throw a rational number in there, and the proof to hold true...
The fancy term for a base 10 number system is decimal http://en.wikipedia.org/wiki/Decimal
Also, here is an article on number systems just so you understand them better: http://en.wikipedia.org/wiki/Numeral_system
Also, your ignorance is really shown when you state all "offshoot" number systems use numbers from the decimal system. First off, it's not true, take for exampe hexadecimal which uses 0-9 and A-F. Next, it could be said that decimal takes the numbers from all the other bases (binary, ternary, octal, hexidecimal..etc), but I wouldn't argue that point. I would argue that somewhere in our modern math, we came up with symbols to represent different values, and then applied them to various number systems. For instance, we use the symbols 1,2,3...9, while the romans used I, V, X, L, C, D, M.
You really are just ignorant on all these subjects, you really DON'T understand. Like I said, I wouldn't be ashamed, if someone asked quizzed me on brain surgery, I could try and bullshit it, but I'd sound like an idiot.
Quote: TriplellYou're "equation" (it's more then 1 equation, btw, so it kind of annoys me that you refer to is as a single equation), proves that x = x.
When you are proving something, it doesn't have to hold true for all numbers. For instance, I could create a proof to show that pi is an irrational number. I wouldn't expect to be able to throw a rational number in there, and the proof to hold true...
The fancy term for a base 10 number system is decimal http://en.wikipedia.org/wiki/Decimal
Also, here is an article on number systems just so you understand them better: http://en.wikipedia.org/wiki/Numeral_system
Also, your ignorance is really shown when you state all "offshoot" number systems use numbers from the decimal system. First off, it's not true, take for exampe hexadecimal which uses 0-9 and A-F. Next, it could be said that decimal takes the numbers from all the other bases (binary, ternary, octal, hexidecimal..etc), but I wouldn't argue that point. I would argue that somewhere in our modern math, we came up with symbols to represent different values, and then applied them to various number systems. For instance, we use the symbols 1,2,3...9, while the romans used I, V, X, L, C, D, M.
You really are just ignorant on all these subjects, you really DON'T understand. Like I said, I wouldn't be ashamed, if someone asked quizzed me on brain surgery, I could try and bullshit it, but I'd sound like an idiot.
So, how's my equation doing? You know I've said this on another thread, but you do know you're not the end all of math. I can take this equation to another forum and see what they think. The problem is, unlike your BS, this is a simple equation, that's hard to disprove. Unless, I'm incorrect, and 9.999... + .999... = 10.998.... LOL. Then, my proof would be shot to hell. LOL.
All your proof proves is that 0.999... is 0.999...
x = 0.999...
x + x = 1.999... = 2x
2x - x = x = 0.999... = 1
Wait a second... my "equation" proves that 0.999... is 1. Holy shit...if you plug in any real number, it holds true.
This must be some cutting edge shit. Quickly, ask a professor of math if he is impressed with my "equation"...he'll be so impressed that I call my series of equations a single equation as well. LOL
Quote: TriplellPlease...take it to another forum. I bet the results are similiar (unless it's a forum on made up math...then yes, you may get some people who partake in your BS)...
All your proof proves is that 0.999... is 0.999...
x = 0.999...
x + x = 1.999... = 2x
2x - x = x = 0.999... = 1
Wait a second... my "equation" proves that 0.999... is 1. Holy shit...if you plug in any real number, it holds true.
This must be some cutting edge shit. Quickly, ask a professor of math if he is impressed with my "equation"...he'll be so impressed that I call my series of equations a single equation as well. LOL.
Well, if the Wiz doesn't want his forums to be places of mathematical discoveries, it's fine with me. I'll take it elsewhere.
Let me see this one.
x = .999...
x + x = 1.999... = 2x
2x - x = x = .999... = 1
You do know we already know that x = .999... for this equation don't you? How do you get .999... = 1 . Oh, I know, .999... is equal to 1, therefore x = .999... is really 1, so .999... = 1. Great Proof. ROTFL. Didn't I say that's what you've been doing this whole thread. LOL.
I'm sorry, plug in any number and it holds true? Only if you don't put .999... in there. Unless, you just magically change .999... into 1, somehow. Don't bother proving that .999... = 1 just state it very firmly, then everyone will believe you. LOL. Tough guys, I love it. Just tell your kids it's so, because you said it's so. Great proof, triplell. NO wait BS the kids, just hope they never learn anything, that'll work.
Hey, by the way, didn't I get booted for 7 days for saying sh**. You've said shit twice now, and added a few personal insults along the way, and haven't gotten suspended yet. Not that I care, but in fairness... I guess if you don't tell anyone you've been drinking, you will get taken seriously. I'll remember that on the next forum.
P.S Scary pic, by the way. He doesn't have a body, though. How's he going to fight?
Geez I really want to erase that P.S. but I'm done here, tonight. And, after that last BS post, I just don't really care.
Quote: JyBrd0403
So, 9.999... + .999... = 10.999... and you can't change the damn .999... into 1, because this equation is an offer of proof, and not some BS debate, where you can just change one number into another at will.
Just subtract 9.999... from both sides. What do you get? 0.999... = 1
Quote:P.S I didn't appreciate being taught by you and your teachers, myself.
It is obvious to anyone by now that you did not appreciate being taught. I feel sorry for you, for that reason.
Quote: JyBrd0403
Well, if the Wiz doesn't want his forums to be places of mathematical discoveries, it's fine with me. I'll take it elsewhere.
Let me see this one.
x = .999...
x + x = 1.999... = 2x
2x - x = x = .999... = 1
You do know we already know that x = .999... for this equation don't you? How do you get .999... = 1 . Oh, I know, .999... is equal to 1, therefore x = .999... is really 1, so .999... = 1. Great Proof. ROTFL. Didn't I say that's what you've been doing this whole thread. LOL.
Let me try to explain this to you. I'll go slow. Bear with me.
2x - x is obviously x, correct?
As stated on the line above, 2x is is 1.999...
1.999... - 0.999... = 1, which is 2x - x which is x, which two lines above, we defined as 0.999...
So, no, sorry, I didn't magically make 0.999... 1. Don't get mad because you don't understand it. The rest of us do.
I've been trying really hard to get you understand the simple concepts of algebra. I just seem unable to reach you.
Quote: TriplellLet me try to explain this to you. I'll go slow. Bear with me.
2x - x is obviously x, correct?
As stated on the line above, 2x is is 1.999...
1.999... - 0.999... = 1, which is 2x - x which is x, which two lines above, we defined as 0.999...
So, no, sorry, I didn't magically make 0.999... 1. Don't get mad because you don't understand it. The rest of us do.
I've been trying really hard to get you understand the simple concepts of algebra. I just seem unable to reach you.
Hate to inform you. But, you didn't prove .999... is equal to 1. Once again, you proved your equation doesn't work. You failed to prove x = .999...
Quote: Triplell
x = 0.999...
x + x = 1.999... = 2x
2x - x = x = 0.999... = 1
While this "proof" seems cute, it is still wrong.
The 2x needs to end with a 8 since you are multipling 9 * 2.
As soon as you do that your 1 becomes .999... again.
Quote: ALFERALFER
The 2x needs to end with a 8 since you are multipling 9 * 2.
Where is the end, and I'll put an 8 in that position.
Quote: CrystalMathWhere is the end, and I'll put an 8 in that position.
obviously at
+ 1....Quote: CrystalMathWhere is the end, and I'll put an 8 in that position.
My point exactly.
Given x=0.999...
Both of these statements are not true.
x + x = 1.999...
2x = 1.999...
Using them as "Proof" is just a waste of time.
Quote: ALFERALFERMy point exactly.
Given x=0.999...
Both of these statements are not true.
x + x = 1.999...
2x = 1.999...
Using them as "Proof" is just a waste of time.
What I said will only prove your point if, and only if, you can tell me exactly where to write the 8. If you can't identify where to put the 8, then we are left with but a series of 9s.
Most of us can't deal with multiple algebra equations.
Just use simple logic and the infinite geometric series formula to show what the repeating decimal is a finite number (a fraction).
.999... =
the first 9 = 9/10^1 (.9) +
the second 9 = 9/10^2 (.09) +
the third 9 = 9/10^3 (.009) + to infinity
all 7th grade math students know the infinite geometric series formula is
a/1-r (most can not prove it without a book)
a = first value in series. Simple .9 or 9/10
and 1 - r or the ratio. That is .1 or 1/10
9/10 / 1 - 1/10
= 9/10 / 9/10
= 1/1
Those that disagree must then prove that the infinite geometric series formula is false.
They can't
Quote: 7crapsIMO, The confusion is when one uses algebra formulas to prove what .999... is.
Most of us can't deal with algebra formulas.
Just use simple logic and the infinite geometric series formula to show what the repeating decimal is as a finite number (a fraction).
.999... =
the first 9 = 9/10^1 (.9) +
the second 9 = 9/10^2 (.09) +
the third 9 = 9/10^3 (.009) + to infinity
all 7th grade math students know the infinite geometric series formula is
a/1-r (most can not prove it without a book)
a = first value in series. Simple .9 or 9/10
and 1 - r or the ratio. That is .1 or 1/10
9/10 / 1 - 1/10
= 9/10 / 9/10
= 1/1
Those that disagree must then prove that the infinite geometric series formula is false.
They can't
I would argue that the infinite geometric series formula is algebra, but either way, I agree.
I had to edit my post. ThanksQuote: TriplellI would argue that the infinite geometric series formula is algebra, but either way, I agree.
South Park is now on!
Quote: 7crapsall 7th grade math students know the infinite geometric series formula is
a/1-r (most can not prove it without a book)
a = first value in series. Simple .9 or 9/10
and 1 - r or the ratio. That is .1 or 1/10
9/10 / 1 - 1/10
= 9/10 / 9/10
= 1/1
Those that disagree must then prove that the infinite geometric series formula is false.
They can't
1/1 is a fraction. If you want to say it can represent .999... or 1 that's fine with me. It doesn't show that .999... and 1 have the same value.
Here's something else, when we add .999... + .999... you've pointed out that there should be an 8 at the end of the number, it's just that the number is cut off at the limit of infinity. But, you can logically see, that this particular .999... will never equal 1. If it were somehow carried out past infinity, the number would eventually end with an 8. So, that's another proof that .999... is not equal to 1.
Quote: JyBrd04031/1 is a fraction. If you want to say it can represent .999... or 1 that's fine with me. It doesn't show that .999... and 1 have the same value.
Here's something else, when we add .999... + .999... you've pointed out that there should be an 8 at the end of the number, it's just that the number is cut off at the limit of infinity. But, you can logically see, that this particular .999... will never equal 1. If it were somehow carried out past infinity, the number would eventually end with an 8. So, that's another proof that .999... is not equal to 1.
This might be hard to wrap your brain around, but infinity isn't a number, it's a concept. There is no "past infinity", as infinity is endless...no edge! (Nerd Fighters Joke)...
All repeating decimals represent a rational number. What rational number represents 0.999... ? If you can give me any value that doesn't equate to one, then that would prove that 0.999 is not equal to 1.
Here is an example of how you turn a repeating decimal into its fraction representation:
0.45454545... = x
100x = 45.454545...
100x - x = 45.454545... - 0.454545....
99x = 45
x = 45/99 which simiplifies to 5/11 (which if you enter into your calculator, you'll find to be 0.454545...)
Quote: TriplellThis might be hard to wrap your brain around, but infinity isn't a number, it's a concept. There is no "past infinity", as infinity is endless...no edge! (Nerd Fighters Joke)...
All repeating decimals represent a rational number. What rational number represents 0.999... ? If you can give me any value that doesn't equate to one, then that would prove that 0.999 is not equal to 1.
You're right, infinity is a concept. As I stated, .999... is cut off at the limit of infinity, so we agree, there is no "past infinity". Infinity isn't necessarily endless, though. It is however, the limit for repeating decimals. You might have a problem wrapping your head around this, but, logically speaking, .999... + .999... has no chance of ever equaling 1.
You can say 1/1 represents .999... it's fine with me. Hey, 1/1, can also represent 1 if you prefer, it's fine with me. If you want to have some fun, let 1/1 = 22 also. It's fine with me, since we're not going to divide this number anyway, we're just going to say it's .999... might as well have some fun and let 1/1 = 22.
Quote: JyBrd0403...logically speaking, .999... + .999... has no chance of ever equaling 1.
I will agree with this
Quote: TriplellI will agree with this
You know what I mean. .999... + .999... will never equal 1.999... or .4999... + .4999... = .999... and has no chance of ever equaling 1.
That should be .999... + .999... = 1.999... and will never equal 2.
Quote: JyBrd0403You know what I mean. .999... + .999... will never equal 1.999...
...
That should be .999... + .999... = 1.999...
I guess, there is a universe somewhere where this makes sense ...
Quote: weaselmanI guess, there is a universe somewhere where this makes sense ...
I'll agree with 0.999... + 0.999 = 1.999... as well.
and 1.999... + 0.999... = 2.999... ; Do you agree with that?
Quote: TriplellI'll agree with 0.999... + 0.999 = 1.999... as well.
and 1.999... + 0.999... = 2.999... ; Do you agree with that?
Not sure if you're asking me this question, or weaselman, but here's my answer.
.999... + .999 (I see this as being 3 - 9's and not infinite 9's since I don't see any ... at the end) = 1.998999...
So, I would disagree with your answer of 1.999...
1.999... + .999... = 2.999...
This I agree with.
Quote: JyBrd0403Not sure if you're asking me this question, or weaselman, but here's my answer.
.999... + .999 (I see this as being 3 - 9's and not infinite 9's since I don't see any ... at the end) = 1.998999...
So, I would disagree with your answer of 1.999...
1.999... + .999... = 2.999...
This I agree with.
Yeah, I forgot the ...
Anyway, if you agree that 1.999... + .999... = 2.999...
Could you answer: What is 2.999... - 0.999... ?
Quote: TriplellYeah, I forgot the ...
Anyway, if you agree that 1.999... + .999... = 2.999...
Could you answer: What is 2.999... - 0.999... ?
2.999... - .999... = 2
Quote: JyBrd04031.999... + .999... = 2.999...
Quote: JyBrd04032.999... - .999... = 2
And you agree that if (x + y = z) then (z - y = x) ?
Quote: TriplellAnd you agree that if (x + y = z) then (z - y = x) ?
I do agree with this.
Quote: TriplellQuote: JyBrd04031.999... + .999... = 2.999...
Quote: JyBrd04032.999... - .999... = 2
And you agree that if (x + y = z) then (z - y = x) ?Quote: JyBrd0403I do agree with this.
and does (x = x)?
Quote: Triplelland does (x = x)?
Yes, x is equal to x .
Quote: TriplellQuote: JyBrd04031.999... + .999... = 2.999...
Quote: JyBrd04032.999... - .999... = 2
And you agree that if (x + y = z) then (z - y = x) ?Quote: JyBrd0403I do agree with this.
and does (x = x)?Quote: JyBrd0403Yes, x is equal to x .
So then, let's get to this and see if we can get you to either 1. Contradict yourself 2. Surprise me
Let's define the following:
x = 1.999...
y = 0.999...
z = 2.999... = x + y (which you stated, see the first quote)
z - y = x (you agreed on this)
2.999... - 0.999... = 2 (you agreed on this)
2 = 1.999... (you agreed on this)
Did you not?
Quote: TriplellSo then, let's get to this and see if we can get you to either 1. Contradict yourself 2. Surprise me
Let's define the following:
x = 1.999...
y = 0.999...
z = 2.999... = x + y (which you stated, see the first quote)
z - y = x (you agreed on this)
2.999... - 0.999... = 2 (you agreed on this)
2 = 1.999... (you agreed on this)
Did you not?
I played along, but I saw this coming.
No, I agreed x = x , or 1.999... = 1.999... I don't recall agreeing that that 2 = 1.999... Your x is still equal to 1.999... when you replace the letters with numbers you get 2 = 1.999... I agree with this. X still equals 1.999... though, (not 2) correct? I don't see anywhere above where you point out x = 2.
Your equation doesn't work, if you're setting out to prove x = x or 1.999... = 1.999...
X must actually be equal to 1.999... or 2 for this equation to work. So, it should be.
x = .999... or 1
y = 1.999... or 2
z = 2.999.. or 3
Of course, if you did that it wouldn't be a proof that .999... is equal to 1. It would just be a statement that x = .999.. or 1. Also, you can't really define x as having 2 different values, can you? Let's try it.
x = 2 or 7
y = 1 or 15
x = 3 or 27
It will start messing up a lot of equations if you're allowed to do that.
Now, if you use my equation, you don't have these kind of problems.
x = .999...
10x = 9.999...
10x + x = 9.999... + .999...
11x = 10.999...
x = .999...
x is equal to .999...
I'm sure you're familiar with Ockham's razor.
Quote: JyBrd0403I played along, but I saw this coming.
No, I agreed x = x , or 1.999... = 1.999... I don't recall agreeing that that 2 = 1.999... Your x is still equal to 1.999... when you replace the letters with numbers you get 2 = 1.999... I agree with this. X still equals 1.999... though, (not 2) correct? I don't see anywhere above where you point out x = 2.
...
x = 2 because you said that z - y = x.
z is 2.999...
y is 0.999...
so what is x?
Put it this way: You are trying to say that
1.999... + 0.999... - 0.999... is sometimes 1.999... and sometimes 2. I'm sorry, but you are the one saying "this" or "that"...not I..
There is no other number, where if you define it, where z + x - x is anything other then z. However, you are trying to prove otherwise. What rule is that exactly?
Quote: JyBrd0403You're right, infinity is a concept. As I stated, .999... is cut off at the limit of infinity, so we agree, there is no "past infinity". Infinity isn't necessarily endless, though. It is however, the limit for repeating decimals.
This was amusing. A non rational number being cut off at the "limit" of infinity. Infinity isn't endless.....actually, it is.
I argue, that in theoretical mathematics, that infinity is not a limit, rather it represents the opposite of a limit. (Forget that we are talking about "limits" in the sense of functions. That's all I'll add tonight.
Thread. Die. Please.
Quote: Triplellx = 2 because you said that z - y = x.
z is 2.999...
y is 0.999...
so what is x?
Put it this way: You are trying to say that
1.999... + 0.999... - 0.999... is sometimes 1.999... and sometimes 2. I'm sorry, but you are the one saying "this" or "that"...not I..
There is no other number, where if you define it, where z + x - x is anything other then z. However, you are trying to prove otherwise. What rule is that exactly?
I understand what you're saying here. But, x = 1.999... because you defined it as such. Then x = 2 because z - y = x correct? So, x = 2 now, and not what you defined it as, which is x = 1.999...
Your equation doesn't work for repeating decimals, unless you care to define x at the beginning as being x = 1.999... or 2. Which again, if you did that, it would no longer serve as a proof that 1.999... is equal to 2.
Your really missing the fun in these repeating decimals. x = 1.999... but the equation you did, although not a proof that 1.999... equals 2, does give a surprising answer. But, a proof that 1.999.. is equal to 2, is a very different thing then just any equation that gives you a surprising answer. For a proof x is already defined, all you try to do is show that x is the same number it was defined as.
I know why you don't want to define x as 1.999... or 2. But, that's what you have to do for your equations to work.
We've already went through the fact that 1.999... + .999... = 2.999... and 1.999... + 1 = 2.999...
These repeating decimals will get you some interesting results. But, my equation is still showing that .999... is equal to .999... and not 1.
Your equations still have x being defined as .999... and then, are not able to prove that fact. I really don't know how you could prove that .999... is in fact equal to itself and also a different number at the same time. I can't see any equation that would give the result of .999... or 1. But, it is possible to show that .999... is indeed equal to .999... And, that 1 is indeed equal to 1.
1 + 0.999... = 1.999...
1.999... + 0.999... = 2.999...
2.999... - 0.999... = 2
or all of this in one equation: 1.999... + 0.999... - 0.999... = 2
But wait: if you do this: 1.999... + (0.999... - 0.999...) = 1.999...
But order of operations (third grade...if you don't understand this..there is no hope), says that it doesn't matter what order you add or subtract in, the answer should always be the same.
Seriously, I love your responses...I literally can't wait for this one. It's as if I'm Bill Gates, and I'm asking you how windows works, and you have no basic understanding of the operating system, however you go ahead and try to tell me I'm wrong anyway. This thread won't die, because I won't let it. This is too entertaining...
Quote: Triplell
or all of this in one equation: 1.999... + 0.999... - 0.999... = 2
But wait: if you do this: 1.999... + (0.999... - 0.999...) = 1.999...
But order of operations (third grade...if you don't understand this..there is no hope), says that it doesn't matter what order you add or subtract in, the answer should always be the same.
Crazy repeating decimals. Two different answers to the same equation, that's crazy! Fun though, huh.
Now all you have to do is say 1.999... + .999... - .999... = 1.999... or 2.
Quote: TriplellNope, 1.999... AND 2.
Look, I've already said in an earlier post, it's really semantics. But, 1.999... can't possibly be both 1.999... and 2 at the same time. You have to choose one or the other.
If you say it 2 then it's 2. If you say it's 1.999... it's 1.999... either one is valid. But, you'll have a hard time doing equations with 1.999... and 2 at the same time.
1.999... 2 + 3 = 4.999... 5 It just doesn't work. You have to choose one or the other.
2 + 3 = 5.
or
1.999... + 3 = 4.999....
They truly are 2 different numbers, and not the same number.
Much like 1.5 is the same as 3/2 or 1.0 is the same as 1.000, 0.999... is the same as 1.
and 4.999 is the same as 5. and 4.49999... is the same as 4.5
Seriously, I promise you I'm not making this shit up. And I'm not agreeing with literally EVERY other mathematician just to agree with them...
Quote: TriplellNo, and this is what you don't understand.
Much like 1.5 is the same as 3/2 or 1.0 is the same as 1.000, 0.999... is the same as 1.
and 4.999 is the same as 5. and 4.49999... is the same as 4.5
Seriously, I promise you I'm not making this shit up. And I'm not agreeing with literally EVERY other mathematician just to agree with them...
I understand, but, you do know the earth wasn't round for thousands of years, too.
2 + 3 = 5
1.999... + 3 = 4.999...
If you want 4.999... to equal 5, you're going to have to round that number off.
1.999... + .999... - .999... = 1.999... or 2.
If you want 1.999... to equal 2, you're going to have to round that number off.
You're rounding all these numbers off.
Quote: JyBrd0403I understand, but, you do know the earth wasn't round for thousands of years, too.
2 + 3 = 5
1.999... + 3 = 4.999...
If you want 4.999... to equal 5, you're going to have to round that number off.
1.999... + .999... - .999... = 1.999... or 2.
If you want 1.999... to equal 2, you're going to have to round that number off.
You're rounding all these numbers off.
You're rounding these off...The rest of us understand that they are the same number...
BUT PLEASE NOTE:
The good news, is that you will literally never have to worry about the situation coming up when you are doing math, as there are no numbers you could ever add up to get 0.999...
Quote: Triplell
The good news, is that you will literally never have to worry about the situation coming up when you are doing math, as there are no numbers you could ever add up to get 0.999...
Sure, there are!
1/3 + 1/3 + 1/3 = 0.333... + 0.333... + 0.333 ... = ?
Quote: weaselmanSure, there are!
1/3 + 1/3 + 1/3 = 0.333... + 0.333... + 0.333 ... = ?
I was going to make a point that any repeating decimal could be mapped to a fraction, which would equate to 1.
I meant "you" in a very specific context as referring to Jy...
I should also note that this is my point. The answer is so obviously 1, and also so obviously 0.999..., however he doesn't believe it could be both. This is mainly due to the fact that he believes that both refers to seperate numbers when in reality, it's just another notation for the same number.
I love his "The world was thought to be flat..." analogy as well. For one, it's actually a pretty common misconception, as most "educated" persons acknowledged a spherical earth. Additionally, there are still religious groups today that believe the earth to be flat.
Quote: Triplell
I should also note that this is my point. The answer is so obviously 1, and also so obviously 0.999..., however he doesn't believe it could be both. This is mainly due to the fact that he believes that both refers to seperate numbers when in reality, it's just another notation for the same number.
I think, he is just trolling. This has been said (directly to him) several times, but "he is a tough man", immune to the reality and logic. "Tough men" never change their opinions, they just go on ... and on ...
Quote: TriplellNope, 1.999... AND 2.
So, where were we at. Oh yes.
1.999... + .999... - .999... = 1.999...
1.999... + .999... - .999... = 2
So, 1.999... + .999... - .999... = 1.999... AND 2.
This equation gives 2 DIFFERENT answers. 1.999... AND 2.
Since you acknowledge we get 2 different answers, you acknowledge that 1.999... and 2 are 2 different numbers, otherwise you would only have 1 answer to the equation 2 or 1.999... whichever you choose.
We have an apple AND an orange. 2 fruits.
A dog AND a cat. 2 animals.
An egg AND another egg. 2 eggs.
1.999... AND 2 . 2 numbers.
