.999~ = 1, Agree?

[diebitter]

I am pretty amazed actually. I never ever came across the concept that .999... was the same as 1. We're taught in British schools (or at least I was) that infinite series are approximations.

0.333... isn't really 1/3 for example, but good enough. And the proof of this was that 0.9999... <> 1!!!

Can any UKers remember this from school?

[strunks]

[ QUOTE ]
It is irrelevant what level of math this is. To call someone pathetic simply for not grasping a concept is incredibly weak.

[/ QUOTE ]

Of course it's relevant. You can't expect everybody to understand hard university level stuff because not everybody has the opportunity or the motivation to learn it. However, there definitely is a point where the level of difficulty of a concept is low enough that it really should be common knowledge.

Whether that point is above or below 7th grade math, I suppose, is up for debate. I'm of the opinion that 7th grade math should be common knowledge. Especially on this board.

[Homer]

[ QUOTE ]
[ QUOTE ]
It is irrelevant what level of math this is. To call someone pathetic simply for not grasping a concept is incredibly weak.

[/ QUOTE ]

Of course it's relevant. You can't expect everybody to understand hard university level stuff because not everybody has the opportunity or the motivation to learn it. However, there definitely is a point where the level of difficulty of a concept is low enough that it really should be common knowledge.

Whether that point is above or below 7th grade math, I suppose, is up for debate. I'm of the opinion that 7th grade math should be common knowledge. Especially on this board.

[/ QUOTE ]

I didn't say it shouldn't be understood. I said it was weak to call someone who doesn't understand "pathetic."

[strunks]

[ QUOTE ]
I am pretty amazed actually. I never ever came across the concept that .999... was the same as 1. We're taught in British schools (or at least I was) that infinite series are approximations.

0.333... isn't really 1/3 for example, but good enough. And the proof of this was that 0.9999... <> 1!!!

Can any UKers remember this from school?


[/ QUOTE ]

If the decimal is cut off at some point like 0.333333333333333333 then it is an approximation. Once you put a bar over it and it goes infinite it's not an approximation anymore. It's exactly 1/3 in decimal notation.

I think people are just confused by the notation. They don't LOOK the same so intuitively they think they are not the same. But really they are.

[LearnedfromTV]

[ QUOTE ]
I am pretty amazed actually. I never ever came across the concept that .999... was the same as 1. We're taught in British schools (or at least I was) that infinite series are approximations.

0.333... isn't really 1/3 for example, but good enough. And the proof of this was that 0.9999... <> 1!!!

Can any UKers remember this from school?


[/ QUOTE ]

.333333... repeating is properly defined as the limit of the infinite series 3/10 + 3/100 + 3/1000 + ...

The way limit is defined is what solves the problem of infinitesimals for us. A few people have discussed this in varying degrees of depth already. As far as we are concerned, "the limit" is a construct that allows us to set a convergent series equal to the number that its partial sums (.3, .33, .333, .3333, etc) seem to be approaching but never getting to. (How that definition works and why it is consistent with a lot of other mathematics is interesting but not material here).

The key is that that what makes numbers like .3333..... "work" or "make sense" mathematically in the sense of cohering with the rest of mathematics as best as possible is that the "..." is defined in terms of limits.

[graydot]

[ QUOTE ]
I am pretty amazed actually. I never ever came across the concept that .999... was the same as 1. We're taught in British schools (or at least I was) that infinite series are approximations.

0.333... isn't really 1/3 for example, but good enough. And the proof of this was that 0.9999... <> 1!!!

Can any UKers remember this from school?


[/ QUOTE ]

Are you serious? So in the UK 1/3 is not .3 Repeating?

[diebitter]

[ QUOTE ]
[ QUOTE ]
I am pretty amazed actually. I never ever came across the concept that .999... was the same as 1. We're taught in British schools (or at least I was) that infinite series are approximations.

0.333... isn't really 1/3 for example, but good enough. And the proof of this was that 0.9999... <> 1!!!

Can any UKers remember this from school?


[/ QUOTE ]

If the decimal is cut off at some point like 0.333333333333333333 then it is an approximation. Once you put a bar over it and it goes infinite it's not an approximation anymore. It's exactly 1/3 in decimal notation.

I think people are just confused by the notation. They don't LOOK the same so intuitively they think they are not the same. But really they are.

[/ QUOTE ]

If that's commonly accepted definition of an infinite series, so be it. A definition is a definition. I was taught otherwise (I think - it's been a long time!), am I still a moran?

To be honest, when I kept seeing 0.999...=1 everywhere, I thought all the writers of that were morans too, but was too polite to be rude about it.

So I guess you win, huh? [img]/images/graemlins/grin.gif[/img]

[Stevolution]

[ QUOTE ]
[ QUOTE ]
I am pretty amazed actually. I never ever came across the concept that .999... was the same as 1. We're taught in British schools (or at least I was) that infinite series are approximations.

0.333... isn't really 1/3 for example, but good enough. And the proof of this was that 0.9999... <> 1!!!

Can any UKers remember this from school?


[/ QUOTE ]

Are you serious? So in the UK 1/3 is not .3 Repeating?

[/ QUOTE ]

Of course it is to a mathematician. Are you asking such a dumb question just to be patronising?

[diebitter]

[ QUOTE ]
[ QUOTE ]
I am pretty amazed actually. I never ever came across the concept that .999... was the same as 1. We're taught in British schools (or at least I was) that infinite series are approximations.

0.333... isn't really 1/3 for example, but good enough. And the proof of this was that 0.9999... <> 1!!!

Can any UKers remember this from school?


[/ QUOTE ]

Are you serious? So in the UK 1/3 is not .3 Repeating?

[/ QUOTE ]
Sheesh. It's taught as an approximation that's as near as you can get. Was that not clear in the statement [ QUOTE ]
We're taught in British schools (or at least I was) that infinite series are approximations. 0.333... isn't really 1/3 for example, but good enough.


[/ QUOTE ]

Should I stick to monosyllables (sorry, "small words") next time? [img]/images/graemlins/grin.gif[/img]

(just kidding ya - my "deliberately obtuse" detector went apeshit at your message, and you needed a bit of kidding for ya nit-picking)

PS: I do remember specific lessons on this, but I really feel uncomfortable representing the whole UK on this matter. Maybe it was my school/teacher, I dunno. (Don't bother with the moran jokes, I've a PhD, so blow that out yer ass).

[strunks]

[ QUOTE ]
If that's commonly accepted definition of an infinite series, so be it. A definition is a definition. I was taught otherwise (I think - it's been a long time!), am I still a moran?

To be honest, when I kept seeing 0.999...=1 everywhere, I thought all the writers of that were morans too, but was too polite to be rude about it.

So I guess you win, huh? [img]/images/graemlins/grin.gif[/img]

[/ QUOTE ]

It doesn't make you a moron to be taught the wrong thing back in the day. You are also not a moron if you can change your opinion when faced with convincing evidence contrary to what you thought.

The morons are the ones who, despite being shown clear evidence that they are wrong, still insist that they are right while not offering any solid reasoning why.

You are not in that category. The ones in that category have stopped reading already.