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1.9999… = 2

Wait until the economists see it. I’m sure they can come up with 1250 = 2.
Posted 9 years agoUntrue. Rounding is just an appoximation for convenience of writing/typing.
Posted 9 years agodepends 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) 2x = 2then yes the answer is 2.
Posted 9 years agoAs above, it doesn’t equal 2 it’s rounded up to 2.
Posted 9 years agoIf you mean 1.9999.. with the 9s going on forever then that does equal 2.
Posted 9 years agoWell.. 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 9 years agoSurely 1.99 recurring approaches 2, but does not equal it.
Posted 9 years ago1/3 = 0.333 recuring
Posted 9 years ago
2/3 = 0.666…
3/3 = 0.999…
4/3 = 1.333…
5/3 = 1.666…
6/3 = 1.999…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 9 years agoRecurring 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 9 years agoBut 10x – x cannot be 9x because x is not 1.0
Posted 9 years agoYes they are exactly the same number
Posted 9 years agoGreenK – Member
But 10x – x cannot be 9x because x is not 1.0
agreed 10xx does not equal 9x
Posted 9 years ago
edit; hang on im confused
2nd edit; im totally down with you ewan now ðŸ˜€
that pickles my brain thoughJust 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
Posted 9 years agowas it an englishman, irishman and a scotsman type of joke???? ðŸ™‚
Posted 9 years agoOf 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 9 years agoYeah but…someone gives some change and it doesn’t add up ??
Posted 9 years agoRight…
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…
Posted 9 years agoHave you looked down the back of the sofa?
Posted 9 years agoI found a pen and some sweets, but no money…
Posted 9 years agoAh 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 9 years agoMany thanks! ðŸ™‚
Posted 9 years agothe scotsman, did you check his pockets??????
Posted 9 years agoalso what are 3 men doing in one hotel room???
Posted 9 years ago1.9 recurring = 2, by definition I think!
Posted 9 years ago
I love infinity. I’m off to read up on Hilbert’s hotel.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?
Posted 9 years agoIf we’re talking infinity, are there more fractions or decimal numbers – and can you prove it?
Posted 9 years agoAssuming 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
Posted 9 years ago
.
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.can you cut a piece of titanium (for example) exactly 1.9 recurring cms long? no you cant.
Posted 9 years ago
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.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 9 years agoAh, good old William of Occam! Or Ockham?
Posted 9 years agoWell.. 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 9 years ago
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