/sci/ - Science & Math

The limit as n approaches infinity of (1/2)^n is 0. But there isn't a particular value of n for which it equals zero.

>>11754007
The limit is never reached.

>>11754008
Limits aren't moving things. They aren't physical processes you have to carry out for a certain amount of time. It makes no sense to say a number is not reached by a number. The infimum of the sequence (1/2, 1/4, 1/8, 1/16, ...) is 0, therefore the limit is 0.

>>11754037
>The infimum of the sequence (1/2, 1/4, 1/8, 1/16, ...) is 0, therefore the limit is 0.
why is it defined this way?

>>11754207
error can be made as small as desired passed a certain threshold in the sequence. if you are curious you should read

Principles of Mathematical Analysis - Walter Rudin

It discusses these things.

>>11753998
><1 equals 1
nope

>1/inf=0
yes, everyday school example:

[math] \displaystyle
\lim_{x \to \infty} \dfrac{x+1}{x} =
\lim_{x \to \infty} 1+ 1/x = 1+0 = 1
[/math]

>>11753998
This argument in OP doesn't make the slightest lick of sense.

>>11754208
i really like this book, thanks

>>11754008
define what "limit being reached" means in mathematical terms and explain why is it relevant/important

>>11753998
For the last time /sci/ infinity isn't real.

>>11755271
it sure is handy though

>>11755271
What do you mean by infinity? Are you saying the natural numbers don't form a set?

>>11755271
Infinity is real. Infinity isn't a never ending quantity but is a placeholder for an unknown amount. Infinity has just as much of a chance to be 1 as any other amount.

>>11755312
>Infinity has just as much of a chance to be 1 as any other amount.
lolno
inf>R

>>11754008
The limit is the number that isnt reached by an approximation. It doesnt matter if its an actual point in the function or not. I dont understand why people argue about limits when they clearly dont even know about any proofs of limits...

>>11755318
It cannot be ruled out as a possibility because doing so would in itself define the value of greater than 1.

>>11753998
The limit of 1/(2^x) as x goes to infinity is absolutely 0.

>>11755280
>>11755312
Something can't go on forever. Simple as.

>>11755336
idiot

>>11755459
ok tell us the last integer then

>>11755271
>infinity isn't real.
Praise be to Yahweh, the child-burning volcano god! Hallelujah!

>>11755707

>>11755707
>Fully Native European worldview unassauged by christian ideas
What remote untouched corner of Europe is like that at all? I find it seriously hard to believe there could ever be any such place. Sounds like a really obscure place, I don't know if an almost completely isolated community can both have access to our mathematical tradition but not to the christian worldview that influenced the development of it's whole surrounding area for a millenium.
Anyway, what does religion have to do with mathematics?

>>11755707
I'm a Slavic Jew and I have a math degree and accept that our common definitions of limits all agree that the real represented by 0.9... is equal to 1.

>>11753998
yes [eqn]
\lim_{n\to\infty} \frac{1}{2^n} = 0
[/eqn]

>>11755707
>native european
The true native europeans, the neanderthals, went extinct a long time ago.

>>11755271
draw a line of finite length. let one end correspond to 0, and the other to 1. segments of the line that don't start and end at 0 and 1 correspond to the real numbers between 0 and 1.
congratulations, you have created a physical manifestation of the uncountable infinity

>>11753998
Yes.

>>11756239
Yes, this, basic math

>>11756363
>draw a line of infinite length
Cannot be done, stopped reading there

>>11758121
who are you quoting ?