1.9999… = 2
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 ago
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 9 years ago
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 9 years ago
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 9 years agojahwombleMember
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 canPosted 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.IanMunroMember
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.
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