0.999999999.... = 1? Watch

Kolya
Badges: 14
#41
Report 11 years ago
#41
(Original post by fusionskd)
999r = infinite hmmmm...its funny but that does kind of make sense.......Who can disprove it?
I can't disprove anything you haven't defined. By your reasoning, I could say "4 = boogiewoogieloo". Who can disprove this?
quote
reply
fusionskd
Badges: 8
Rep:
?
#42
Report 11 years ago
#42
infinite=an endless quantity without any boundries or limits...
999r=an endless quantity...
0
quote
reply
Overmars
Badges: 15
Rep:
?
#43
Report 11 years ago
#43
(Original post by Lusus Naturae)
What is this "\infty" you talk about? Define it for me!
Ah, gotcha! :p:
0
quote
reply
Kolya
Badges: 14
#44
Report 11 years ago
#44
(Original post by fusionskd)
infinite=an endless quantity without any boundries or limits...
999r=an endless quantity...
Well, logically speaking, that is correct. If A = C and B = C then A=B. Mathematically speaking, your definition of infinity is too unrigourous for my tastes.
quote
reply
The Bachelor
Badges: 12
Rep:
?
#45
Report 11 years ago
#45
(Original post by Synergetic)
I'm guessing 9999r = infinity, then?
9999r hasn't been defined yet, but under the simplest interpretation, this is simply the sum \displaystyle \sum_{n=1}^{\infty} 9*10^{n}, which of course diverges to +\infty.

Keep in mind, however, that 9999r is not an integer, or a real number, or anything. (An integer/real, to put it short, cannot have infinitely many decimal places left of the decimal point.)


-------------------

I think the most consistent definition of \infty for situations like this is: a sum \displaystyle \sum_{n=1}^{\infty} S_n diverges to \infty iff \forall x \in R^+, \exists N such that \displaystyle \sum_{n=1}^{N} S_n>x (Note: this definition does not exclude the possibility that \displaystyle \sum_{n=1}^{\infty} S_n also diverges to another value.)

But in short, fusionskd is pretty much right. Something is infinite iff it is unbounded (though this is still vague). The definition I provided shows the series is unbounded in the positive direction.
0
quote
reply
Zii
Badges: 13
Rep:
?
#46
Report 11 years ago
#46
I hate it when people treat infinity as a number.
0
quote
reply
Simba
Badges: 15
Rep:
?
#47
Report 11 years ago
#47
(Original post by hamtomilton)
Prove e is transendental.
*Nukes it with the Lindemann–Weierstrass theorem* :p: ...

Consider this one:

a*x = x + x + ... + x (a lots of x).

Similarly:

x*x = x + x + ... + x (x lots of x).

Or equivalently:

x² = x + x + ... + x (x lots of x).

Differentiating:

d(x²)/dx = d(x)/dx + d(x)/dx + ... + d(x)/dx (x derivatives).

2x = 1 + 1 + ... + 1 (x lots of 1).

2x = x.

2 = 1 (provided x =/= 0).

:cool: .
0
quote
reply
Dystopia
Badges: 1
Rep:
?
#48
Report 11 years ago
#48
(Original post by Simba)
d(x²)/dx = d(x)/dx + d(x)/dx + ... + d(x)/dx (x derivatives).
Nice try.

Spoiler:
Show

There are a variable number of 'x's.

Let y = x + x  + ... + x + x (x lots of x)

Then y + \delta y = (x + \delta x) + ... + (x + \delta x)\; \;(x + \delta x \mathrm{\; lots \; of \;} x+\delta x)

y + \delta y = (x+\delta x)^{2}

y + \delta y = x^{2} + 2x \delta x +  (\delta x)^{2}

\delta y = 2x \delta x +  (\delta x)^{2}

\displaystyle \frac{\mathrm{d}y}{\mathrm{d}x} = \lim_{\delta x \to 0} \frac{\delta y}{\delta x} = 2x
0
quote
reply
Ignoramus
Badges: 12
Rep:
?
#49
Report 10 years ago
#49
I simply wish to try everyone's patience here on the Maths forum really

1/3 = 0.33333333...
Therefore 3/3 = 0.99999999... = 1?
0
quote
reply
Sanjetti
Badges: 0
Rep:
?
#50
Report 10 years ago
#50
(Original post by Ignoramus)
I simply wish to try everyone's patience here on the Maths forum really

1/3 = 0.33333333...
Therefore 3/3 = 0.99999999... = 1?
You're testing my patience with your signature :p: ;-) Just kidding

But 0.9 recurring does equal 1, theres some proof for it but I forget
0
quote
reply
fieryiceissweet
Badges: 12
Rep:
?
#51
Report 10 years ago
#51
(Original post by Ignoramus)
I simply wish to try everyone's patience here on the Maths forum really

1/3 = 0.33333333...
Therefore 3/3 = 0.99999999... = 1?
umm yes
for goodness sake i know that and im only 16
dont be surprised if you get a lot of negs for a dumb question which you could have googled
0
quote
reply
RestrictedAccess
Badges: 0
#52
Report 10 years ago
#52
yeh that was drilled into us from year 9 for all of about a lesson, the other proof is:

if x = 0.99999....
10x = 9.99999.....
10x -x = 9
9x = 9
x = 9/9
x=1

so 0.99... = 1
0
quote
reply
Ignoramus
Badges: 12
Rep:
?
#53
Report 10 years ago
#53
Won't be at all surprised about the neg reps!
0
quote
reply
Sick Puppy
Badges: 10
Rep:
?
#54
Report 10 years ago
#54
well duh?
0
quote
reply
luk333
Badges: 1
Rep:
?
#55
Report 10 years ago
#55
(Original post by Ignoramus)
Won't be at all surprised about the neg reps!
Why ask...
0
quote
reply
Kolya
Badges: 14
#56
Report 10 years ago
#56
(Original post by RestrictedAccess)
yeh that was drilled into us from year 9 for all of about a lesson, the other proof is:

if x = 0.99999....
10x = 9.99999.....
10x -x = 9
9x = 9
x = 9/9
x=1

so 0.99... = 1
Isn't that proof a little suspect?
quote
reply
Free Radical VII
Badges: 0
Rep:
?
#57
Report 10 years ago
#57
Chill-out guys. Its not that obvious. i heard someone got that as an oxford interview question
0
quote
reply
Ruthie!
Badges: 16
Rep:
?
#58
Report 10 years ago
#58
BUT if 99.9% of the mass in the universe is unaccounted for..
99.9% = 100%

WE DON'T EXIST!!!!!!!1111oneonetwo
0
quote
reply
Sick Puppy
Badges: 10
Rep:
?
#59
Report 10 years ago
#59
(Original post by Free Radical VII)
Chill-out guys. Its not that obvious. i heard someone got that as an oxford interview question
:eek: well if someone got asked that at an oxford interview...


:woo: :woo: :woo: :woo: :woo: :woo: :woo: :woo: :woo: :woo: :woo: :woo: :woo: :woo: :woo: :woo: :woo: :woo: :woo: :woo: :woo: :woo: :woo:
0
quote
reply
Modulus
Badges: 0
Rep:
?
#60
Report 10 years ago
#60
(Original post by Kolya)
Isn't that proof a little suspect?
Why? It looks fine.
0
quote
reply
X

Quick Reply

Attached files
Write a reply...
Reply
new posts
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise

University open days

  • University of Lincoln
    Mini Open Day at the Brayford Campus Undergraduate
    Wed, 19 Dec '18
  • University of East Anglia
    UEA Mini Open Day Undergraduate
    Fri, 4 Jan '19
  • Bournemouth University
    Undergraduate Mini Open Day Undergraduate
    Wed, 9 Jan '19

Were you ever put in isolation at school?

Yes (199)
27.95%
No (513)
72.05%

Watched Threads

View All
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise