# 0.999999999.... = 1?Watch

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?
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11 years ago
#42
infinite=an endless quantity without any boundries or limits...
999r=an endless quantity...
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11 years ago
#43
(Original post by Lusus Naturae)
What is this "" you talk about? Define it for me!
Ah, gotcha!
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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.
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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 , which of course diverges to .

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.)

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I think the most consistent definition of for situations like this is: a sum diverges to iff , such that (Note: this definition does not exclude the possibility that 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.
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11 years ago
#46
I hate it when people treat infinity as a number.
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11 years ago
#47
(Original post by hamtomilton)
Prove e is transendental.
*Nukes it with the Lindemannâ€“Weierstrass theorem* ...

Consider this one:

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

Similarly:

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

Or equivalently:

xÂ² = x + x + ... + x (x lots of x).

Differentiating:

d(xÂ²)/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).

.
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11 years ago
#48
(Original post by Simba)
d(xÂ²)/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 (x lots of x)

Then

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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?
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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 ;-) Just kidding

But 0.9 recurring does equal 1, theres some proof for it but I forget
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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
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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
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10 years ago
#53
Won't be at all surprised about the neg reps!
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10 years ago
#54
well duh?
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10 years ago
#55
(Original post by Ignoramus)
Won't be at all surprised about the neg reps!
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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?
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10 years ago
#57
Chill-out guys. Its not that obvious. i heard someone got that as an oxford interview question
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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
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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
well if someone got asked that at an oxford interview...

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10 years ago
#60
(Original post by Kolya)
Isn't that proof a little suspect?
Why? It looks fine.
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