Home Forum Chat Forum 1.9999… = 2

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• 1.9999… = 2
• funkynick
Subscriber

Discuss…

ðŸ˜€

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

5thElefant
Member

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

clubber
Member

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

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.

Gary_M
Member

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

djglover
Member

2.49 = 2

1.51 = 2

matthewjb
Subscriber

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

funkynick
Subscriber

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.

glenh
Subscriber

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

Ewan
Member

1.9 recuring equates to 2.

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

IanMunro
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…

Ewan
Member
simonfbarnes
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.

Ewan
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’.

GreenK
Subscriber

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

nickc
Subscriber

Yes they are exactly the same number

colande
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 ðŸ˜€
that pickles my brain though

tyger
Member

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

colande
Member

was it an english-man, irish-man and a scots-man type of joke???? ðŸ™‚

funkynick
Subscriber

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…

tyger
Member

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

funkynick
Subscriber

Right…

Three men go to a hotel and pay the bellboy Â£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 Â£25 for the room tonight and gives the bellboy Â£5 to take back to the men.

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

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

Or something like that…

5thElefant
Member

Have you looked down the back of the sofa?

funkynick
Subscriber

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

GrahamS
Subscriber

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.

tyger
Member

Many thanks! ðŸ™‚

colande
Member

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

colande
Member

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

Cooroo
Member

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

matthewjb
Subscriber

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

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

Â£9 each = Â£27

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

What missing Â£1?

thepurist
Subscriber

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

jahwomble
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.

IanMunro
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.

matthewjb
Subscriber

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

tommytowtruck
Subscriber

Ah, good old William of Occam! Or Ockham?

miketually
Subscriber

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.