Sloth-hybrid
Knight
0.9999... = 1?
yes/no
yes/no
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0.9999... = 1?
- Thread starter Sloth-hybrid
- Start date
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Spriggan-hybrid
Knight
Re: 0.9999... = 1?
no, but 0.99999 dose...
no, but 0.99999 dose...
Dead Head E-Mart
Wanderer
Re: 0.9999... = 1?
this is random
this is random
Sloth-hybrid
Knight
Re: 0.9999... = 1?
0.9999... = 1
Thus x = 0.9999...
10x = 9.9999...
10x - x = 9.9999... - 0.9999...
9x = 9
x = 1.
If you write it on paper it opens a worm hole.
0.9999... = 1
Thus x = 0.9999...
10x = 9.9999...
10x - x = 9.9999... - 0.9999...
9x = 9
x = 1.
If you write it on paper it opens a worm hole.
Re: 0.9999... = 1?
meh.. it's just a loss of precision.
0.9999... = 1 - 10^-infinity
10^-infinity is essentially, but not quite, zero.. thus: 0.9999... != 1.
So it's not that 0.9999... = 1 but that when applying a math shortcut (moving the decimal point once to the right when multiplying by 10) to a repeating number you lose precision. Try carrying out the proper sequence of steps (start multiplying with the final 9.. except that there are an infinite number of them.. so there is no final 9).
You're essentially misapplying the shortcut in the same way that children and possibly some dialects misapply the -ed ending on some verbs when forming the past tense (ie: he runned to the store).
...one of my old HS teachers held the class in awe with this years ago. I say meh.
Edit:
There are other arguments as well, such as...
1/9 = 0.1111...
9(1/9) = 9(0.1111...)
9/9 = 1 = 0.9999....
...but it's faulty for the same argument as above.
meh.. it's just a loss of precision.
0.9999... = 1 - 10^-infinity
10^-infinity is essentially, but not quite, zero.. thus: 0.9999... != 1.
So it's not that 0.9999... = 1 but that when applying a math shortcut (moving the decimal point once to the right when multiplying by 10) to a repeating number you lose precision. Try carrying out the proper sequence of steps (start multiplying with the final 9.. except that there are an infinite number of them.. so there is no final 9).
You're essentially misapplying the shortcut in the same way that children and possibly some dialects misapply the -ed ending on some verbs when forming the past tense (ie: he runned to the store).
...one of my old HS teachers held the class in awe with this years ago. I say meh.
Edit:
There are other arguments as well, such as...
1/9 = 0.1111...
9(1/9) = 9(0.1111...)
9/9 = 1 = 0.9999....
...but it's faulty for the same argument as above.
panDEMONium-hybrid
Sorceror
Re: 0.9999... = 1?
i say yes. mainly because math is for the insane, for example u can make the
number one equate to the number zero...er rather prove that the number one
is actually 0. don't ask me how...just go look it up on internet. i am sure it is
there some where. Oh and while u at that read up on the mandlebrot set
(not sure if spelt correctly). Night!
i say yes. mainly because math is for the insane, for example u can make the
number one equate to the number zero...er rather prove that the number one
is actually 0. don't ask me how...just go look it up on internet. i am sure it is
there some where. Oh and while u at that read up on the mandlebrot set
(not sure if spelt correctly). Night!
MemphisWade
Knight
Re: 0.9999... = 1?
1 = 1
1 = 1
djstepanek
Page
Re: 0.9999... = 1?
your comupter will say .999...=1 because of machine precision so for all practical applications it does indeed = 1.
your comupter will say .999...=1 because of machine precision so for all practical applications it does indeed = 1.
Sloth-hybrid
Knight
Re: 0.9999... = 1?
1/3 = .33333...
2/3 = .66666...
1/3 + 2/3 = .99999...
1/3 + 2/3 = 1
??
1/11 = .0909...
10/11 = .9090...
1/11 + 10/11 = .9999...
1/11 + 10/11 = 1
??
1/3 = .33333...
2/3 = .66666...
1/3 + 2/3 = .99999...
1/3 + 2/3 = 1
??
1/11 = .0909...
10/11 = .9090...
1/11 + 10/11 = .9999...
1/11 + 10/11 = 1
??
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