.999999 = 1
Pic Whore
Joined: Jul 2004
Posts: 22,224
Likes: 1
From: NJ
Originally Posted by Kestrel
So looking at this some more, I think the guy is right (as much of an arrogant prick he is), but his proofs are wrong. Two ways to look at it:
1) Calculus limit
0.99999..... = 1-1/10^x, where x goes to +inf.
lim x->inf (1-1/10^x) = 1
2) Geometric series
0.99999..... = 0.9 + 0.09 + 0.009 + ... + 0.9*1/10^x, where x goes to +inf
sum of a converging geometric series = a/(1-r)
=> 0.9/(1-1/10) = 1
1) Calculus limit
0.99999..... = 1-1/10^x, where x goes to +inf.
lim x->inf (1-1/10^x) = 1
2) Geometric series
0.99999..... = 0.9 + 0.09 + 0.009 + ... + 0.9*1/10^x, where x goes to +inf
sum of a converging geometric series = a/(1-r)
=> 0.9/(1-1/10) = 1
you just proved that the limit of .9 repeating = 1.
Push to shock!
Joined: Sep 2002
Posts: 4,583
Likes: 0
From: Palo Alto, CA
Originally Posted by Jani
he's trying to prove that .9 repeating = 1
you just proved that the limit of .9 repeating = 1.
you just proved that the limit of .9 repeating = 1.
Push to shock!
Joined: Sep 2002
Posts: 4,583
Likes: 0
From: Palo Alto, CA
Originally Posted by Jani
true, but the original question/proof is vague and does not specify if we're dealing with limits.
h:
Pic Whore
Joined: Jul 2004
Posts: 22,224
Likes: 1
From: NJ
Originally Posted by Brar
to me .999999 is not as accurate as 1. It is just another way for people to be lazy and just put 1 instead.
but I'm down :hsughr:
but I'm down :hsughr:
