Hmm...

[Tomm]

if you only say 3 decimal places, such as 0.999 then its obviously a number in its own and doesnt equal 1, did i miss something here?

Sorry, by the ellipsis dots (...) I meant 0.999 recurring. Should have made that clear.

but i quoted someone who said mathmatition say 1 is not the same as 0.9999recurring

No, you quote someone saying:

0.99999999999999999999999999999999999999999

If your a mathmatition - no, its not one

He doesn't say it's recurring, so he's quite right, it's not one.

[sfboy]

Surely its more a question of semantics,

if the = symbol means has the same properties as.

[monkeyseemonkeydo]

thats not silly, i just didnt have a calculator

If you typed the post on a computer (guessing you did) then you did have a calculator... not that you should need one for that anyhoo .

Sorry, back on topic. I'd have thought that technically 0.99 recurring doesn't equal (i.e. ≠) 1, however it approximates to (very closely) therefore you would just replace the = with a squiggly = sign: 0.999... ≈ 1. Or maybe it should be a 'tends to' since the 0.999 stretches to infinity but never reaches it therefore 0.999... → 1.

Edit: Anyone know the proper name for a squiggly equals?... You'd think maybe four years of aerospace engineering and 3 years of a postgrad in aerodynamics would teach you that sort of thing but aparently not

[Joe_Elding]

If you typed the post on a computer (guessing you did) then you did have a calculator... not that you should need one for that anyhoo .

Sorry, back on topic. I'd have thought that technically 0.99 recurring doesn't equal (i.e. ≠) 1, however it approximates to (very closely) therefore you would just replace the = with a squiggly = sign: 0.999... ≈ 1. Or maybe it should be a 'tends to' since the 0.999 stretches to infinity but never reaches it therefore 0.999... → 1.

Edit: Anyone know the proper name for a squiggly equals?... You'd think maybe four years of aerospace engineering and 3 years of a postgrad in aerodynamics would teach you that sort of thing but aparently not

equivalant to? thats how I've always heard them 'said' anyway

[JT!]

Another thing is:

I don't belive that there's such thing as an infitily long number, becuase if you moved your finger from one point to another (say 1 meter) people wil say there are an infinite number of gaps between that movement, if that were true your finger would have to be moving at an infinite speed, which it isn't, it's moving at 150mph tops? Hence there's a certian number of points, all be it a lot of points, there's still a number. Making 0.999... a number which will never exsist anyway.

Therefor you can not cut something up into thirds. One will always be bigger then the other two. Making the fraction 1/3 an impossible number too.

Edited April 5, 2008 by JT!

[JonMack]

Another thing is:

I don't believe that there's such thing as an infitily long number, becuase if you moved your finger from one point to another (say 1 metre) people will say there are an infinite number of gaps between that movement, if that were true your finger would have to be moving at an infinite speed, which it isn't, it's moving at 150mph tops? Hence there's a certian number of points, all be it a lot of points, there's still a number. Making 0.999... a number which will never exsist anyway.

But that's not what is being said. The "finger" is being "moved" forever, if you put a stop on the movement, then there aren't going to be an infinite amount of gaps, there are only going to be so many, no matter how small the gaps are, there's always going to be a limit, but as we're staying its going on forever, then the amount of gaps will be infinite.

I don't know why you've thrown in a measurement of speed, that just adds to your confusion.

Therefor you can not cut something up into thirds. One will always be bigger then the other two. Making the fraction 1/3 an impossible number too.

Cut 3 up into thirds for me please and tell me what you get.

[Ben Jones]

Had this discussion with my maths teacher about this one a while ago.

No matter how much I don't like it, and how hard i found to get my head around it, 0.999* = 1

[ManxTrialSpaz]

Another thing is:

I don't belive that there's such thing as an infitily long number, becuase if you moved your finger from one point to another (say 1 meter) people wil say there are an infinite number of gaps between that movement, if that were true your finger would have to be moving at an infinite speed, which it isn't, it's moving at 150mph tops? Hence there's a certian number of points, all be it a lot of points, there's still a number. Making 0.999... a number which will never exsist anyway.

Therefor you can not cut something up into thirds. One will always be bigger then the other two. Making the fraction 1/3 an impossible number too.

It's not saying the distance is infinetly long, rather than than the measure of precision and accuracy is infinite - 0.999... is an infinitely accurate number, in fact any recurring number is. It' got nothing to do with an infinite length.

Also I do believe that if you have a chocolate bar which is 30cm long, it won't be too hard to cut it up in 10 cm lengths.

You're thinking 1/3 is impossible because a third of 10 is said to be 0.333... even though three 0.333...s is 0.999... The point there is that 10 cannot be divided into thirds but it can be divided into three parts which, when added together, are infinitely close to being 10. - I was trying to say that, even though 10 can't be divided by three, other numbers, such as 3, or 30, can be divided by three.

Edited April 5, 2008 by ManxTrialSpaz

[JT!]

What i'm trying to say is 0.999... doesn't exsist, becuase it's acurate to a decimal that goes byond what ever will be capeable.

[Tomm]

I don't belive that there's such thing as an infitily long number, becuase if you moved your finger from one point to another (say 1 meter) people wil say there are an infinite number of gaps between that movement, if that were true your finger would have to be moving at an infinite speed, which it isn't,

If you say there are an infinite number of 'gaps', then each gap would have to be infinitely small. That doesn't mean the distance between point A and point B is infinite, though. Therefore the speed would NOT be infinite.

[hI-OOPS-CAPS]

the concept of infinity is quite hard to grasp to me, theres no visual image or anything to relate to in everyday life

and 10 can be diveded by 3, whoever said it cant. i suppose the answer is simply 10/3