Discuss...
Well, as we seem to be on a bit of a maths trip today...
Discuss...
Well, as we seem to be on a bit of a maths trip today...
Wait until the economists see it. I'm sure they can come up with 1250 = 2.
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.
As above, it doesn't equal 2 it's rounded up to 2.
2.49 = 2
1.51 = 2
If you mean 1.9999.. with the 9s going on forever then that does equal 2.
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.
Surely 1.99 recurring approaches 2, but does not equal it.
1.9 recuring equates to 2.
Same as 1/2 + 1/4 + 1/8 + 1/16 etc is equal to 1.
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...
Oh dear. http://en.wikipedia.org/wiki/0.999...
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.
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'.
But 10x - x cannot be 9x because x is not 1.0
Yes they are exactly the same number
GreenK - MemberBut 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
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
was it an english-man, irish-man and a scots-man type of joke????
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...
Yeah but...someone gives some change and it doesn't add up ??
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...
Have you looked down the back of the sofa?
I found a pen and some sweets, but no money...
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.
Many thanks!
the scots-man, did you check his pockets??????
also what are 3 men doing in one hotel room???
1.9 recurring = 2, by definition I think!
I love infinity. I'm off to read up on Hilbert's hotel.
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?
If we're talking infinity, are there more fractions or decimal numbers - and can you prove it?
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.
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.
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
Ah, good old William of Occam! Or Ockham?
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