1.9999… = 2

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This topic has 36 replies, 22 voices, and was last updated 15 years ago by miketually.

Viewing 37 posts - 1 through 37 (of 37 total)

1.9999… = 2
funkynick
Full Member

Discuss…

😀

Well, as we seem to be on a bit of a maths trip today…

Posted 15 years ago

5thElefant
Free Member

Wait until the economists see it. I’m sure they can come up with 1250 = 2.

Posted 15 years ago

clubber
Free Member

Untrue. Rounding is just an appoximation for convenience of writing/typing.

Posted 15 years ago

thisisnotaspoon
Free Member

depends on the question

1.9999 does not equal 2, but does round up to it at 1,2,3 and 4 significant figures

however if the question was:
lim (x->0) 2-x = 2

then yes the answer is 2.

Posted 15 years ago

Gary_M
Free Member

As above, it doesn’t equal 2 it’s rounded up to 2.

Posted 15 years ago

djglover
Free Member

2.49 = 2

1.51 = 2

Posted 15 years ago

matthewjb
Free Member

If you mean 1.9999.. with the 9s going on forever then that does equal 2.

Posted 15 years ago

funkynick
Full Member

Well.. I meant it as a recurring.. that’s what the dots were for… unlike those ones which are meant to be an elipsis, but I can’t remember what the alt+code is for them.

Posted 15 years ago

glenh
Free Member

Surely 1.99 recurring approaches 2, but does not equal it.

Posted 15 years ago

Ewan
Free Member

1.9 recuring equates to 2.

Same as 1/2 + 1/4 + 1/8 + 1/16 etc is equal to 1.

Posted 15 years ago

IanMunro
Free Member

1/3 = 0.333 recuring
2/3 = 0.666…
3/3 = 0.999…
4/3 = 1.333…
5/3 = 1.666…
6/3 = 1.999…

Posted 15 years ago

Ewan
Free Member

Oh dear. http://en.wikipedia.org/wiki/0.999…

Posted 15 years ago

simonfbarnes
Free Member

1.9 recuring equates to 2.

well, as a number you can write down 1.99999…. is always going to be less, as you cannot write an infinite number of 9s. And if you’re going to be merely conceptual, then they’re obviously different.

The integers and the real number field are different things. If someone asks, “How many people are in the room?”, the answer cannot have a fractional part, even if one person has a missing leg. Integers count, real numbers measure.

Posted 15 years ago

Ewan
Free Member

Recurring means ‘a real number in the decimal numeral system in which a sequence of digits repeats infinitely’.

Therefore 1.9 recurring does equate to 2. If you could write it down, it wouldn’t be recurring. Unless you had infinite time and resources.

What have integers got to do with anything…? If you’re bothered by the above proof, replace ‘1’ with ‘1.0’.

Posted 15 years ago

GreenK
Free Member

But 10x – x cannot be 9x because x is not 1.0

Posted 15 years ago

nickc
Full Member

Yes they are exactly the same number

Posted 15 years ago

colande
Free Member

GreenK – Member

But 10x – x cannot be 9x because x is not 1.0

agreed 10x-x does not equal 9x
edit; hang on im confused
2nd edit; im totally down with you ewan now 😀
that pickles my brain though

Posted 15 years ago

tyger
Free Member

Just while I’m working this out can someone remind me how the puzzle goes about 3 chaps who each pay £10 for something and there’s a discount and it should be £9 each and a £1 goes missing – or something like that?? Cheers

Posted 15 years ago

colande
Free Member

was it an english-man, irish-man and a scots-man type of joke???? 🙂

Posted 15 years ago

funkynick
Full Member

Of course 10x – x = 9x

If I have ten x’s and remove one x, I have nine x’s… how is that not correct? It’s simple algebra surely…

Posted 15 years ago

tyger
Free Member

Yeah but…someone gives some change and it doesn’t add up ??

Posted 15 years ago

funkynick
Full Member

Right…

Three men go to a hotel and pay the bellboy £10 each for a room for the night. The bellboy then takes the money down to the manager to pay, but the manager says it’s only £25 for the room tonight and gives the bellboy £5 to take back to the men.

He takes the change back to the men, who tell him to give them each £1 and take £2 as a tip, so they each have paid £9 for the room.

But, and this is the problem, if they have each paid £9 for the room, plus the £2 for the bellboy, when you add it all together you get £27 + £2 = £29… when they originally pay £30… so where has the extra £1 gone?

Or something like that…

Posted 15 years ago

5thElefant
Free Member

Have you looked down the back of the sofa?

Posted 15 years ago

funkynick
Full Member

I found a pen and some sweets, but no money…

Posted 15 years ago

GrahamS
Full Member

Ah the joys of infinity.

It’s a bit like claiming that the distance between any two points is infinite because the distance can be halved an infinite number of times.

Posted 15 years ago

tyger
Free Member

Many thanks! 🙂

Posted 15 years ago

colande
Free Member

the scots-man, did you check his pockets??????

Posted 15 years ago

colande
Free Member

also what are 3 men doing in one hotel room???

Posted 15 years ago

Cooroo
Free Member

1.9 recurring = 2, by definition I think!
I love infinity. I’m off to read up on Hilbert’s hotel.

Posted 15 years ago

matthewjb
Free Member

if they have each paid £9 for the room, plus the £2 for the bellboy, when you add it all together you get £27 + £2 = £29… when they originally pay £30… so where has the extra £1 gone?

That’s just adding when you should be taking away though.

£9 each = £27

£2 for the bellboy and £25 for the room =£27

What missing £1?

Posted 15 years ago

thepurist
Full Member

If we’re talking infinity, are there more fractions or decimal numbers – and can you prove it?

Posted 15 years ago

jahwomble
Free Member

Assuming infinitely good eyesight,the required level of fine motor control and a precisely defined enough cutting tool, Occam’s razor may be good here.

can you cut a piece of titanium (for example) exactly 1.9 recurring cms long? no you cant.

can you cut a piece of titanium (for example) exactly 2.0 recurring cms long? yes you can
.
so no ,regardless of what Bertrand Russell and other assorted philosophical mit mots think, they are not exactly the same number at all, they may however be functionally identical numbers, unless the definition you need in your calculation is massively high.

Posted 15 years ago

IanMunro
Free Member

can you cut a piece of titanium (for example) exactly 1.9 recurring cms long? no you cant.
Rather depends on what your dial is marked in. Mine’s mark at 120 degree intervals. So 3 marks per revolution, giving me settings (assuming infinitely good eyesight) of 1/3, 2/3 and 3/3. Now it’s indeniably that 1/3= 0.333…, 2/ =0.666…, 3/3=0.999… etc. So 2.0 turns of my dial yields a 1.999.. cut.

Posted 15 years ago

matthewjb
Free Member

If we’re talking infinity, are there more fractions or decimal numbers

Decimals I think

– and can you prove it?

No it’s a long time since I did any serious pure maths

Posted 15 years ago

tommytowtruck
Full Member

Ah, good old William of Occam! Or Ockham?

Posted 15 years ago

captain_spaulding
Free Member

http://uk.youtube.com/watch?v=Bomv-6CJSfM

Posted 15 years ago

miketually
Free Member

Well.. I meant it as a recurring.. that’s what the dots were for… unlike those ones which are meant to be an elipsis, but I can’t remember what the alt+code is for them.

alt+0133 (using the number pad)

Posted 15 years ago