[ 3 / biz / cgl / ck / diy / fa / ic / jp / lit / sci / vr / vt ] [ index / top / reports ] [ become a patron ] [ status ]
2023-11: Warosu is now out of extended maintenance.

/sci/ - Science & Math

View post   
File: 9 KB, 250x187, 1410788799962.jpg [View same] [iqdb] [saucenao] [google]
6823876 No.6823876[DELETED]  [Reply] [Original]

Why did god make 0.9999...=1?

Is there some kind of message hidden in it?

>> No.6823877

Mathematics is invented, not discovered

>> No.6823878

God didn't do that.
Satan did.

>> No.6823880

yes

>> No.6823892

>>6823876
He didn't. We've just <span class="math"> \underline{ \bf{ DEFINED } }[/spoiler] it as such with an equivalence relation over the decimals so the decimals modulated by it would satisfy the Real Number Axioms and work as a construction of the reals.

/thread

>inb4 retards think this can be proved with arithmetic
>inb4 bigger retards think this can be proved "more rigorously" by unwrapping the definition of decimals into a geometric series
>inb4 the biggest retards think you can use a second construction to prove results of the first before ever showing the first satisfied the real axioms

>> No.6823904

>>6823892
To define it any other way would have led to the limit of the finite sequence of decimals (0.9, 0.99, 0.999, etc) having a different limit to 0.999... which would have been kinda dumb.

>> No.6823905

>>6823904
>different limit to 0.999...
meant different value to 0.999...

>> No.6823911

>>6823892
>Implying dedekind cut construction isn't as valid

oh boy, tell me all about your amazing better math! lets show everyone how much we know and not just make things simple! :^)

>> No.6823912

>>6823892
we didn't define 0.999... in particular, we defined what infinite decimals are. That is the limit of a sequence of finite decimals that share the first n digits with the infinite decimal.

What other definition of infinite decimals do you think would also be valid?

>> No.6823917

this shit again....

>> No.6823920

A horned frog!
The most based of all frogs and the mascot of a Christian College. Coincidence?

>> No.6823943

>>6823912
>>6823904
guys you really make him seem validated in that he thinks kiddies are making awful arguments for .9999... = 1

if what you want to say comes from freshman calc please dont say it

>> No.6823956

>>6823943
It's real analysis 1.

It's not difficult.

>> No.6823961

God doesn't exist.

>> No.6823968

>>6823956
That's the point.

>> No.6823975

>>6823956
I have no idea where you come up with that.
I've yet to see where in the construction of the real numbers we define that.

>> No.6823977

>>6823968
Then why do you think those posts validate his point?

Or did you just do real analysis and think anything without an explicit epsilon proof has to be babby tier?

>> No.6823980

>>6823975
If it's dedekind cuts then right in their definition. A real number is the set of all rational numbers smaller than itself.

>> No.6823984

>>6823904
>limit of the finite sequence of decimals
>limit
>of
>the finite sequence
also
>defining decimals in terms of decimals

Go learn math before commenting on it....

>>6823911
It's valid of course but you cannot refer to it on questions concerning the CONSTRUCTION of decimals.

>>6823912
>That is the limit of a sequence of finite decimals that share the first n digits with the infinite decimal

Limit converging in the set of reals aka decimals. You're making a circular argument.

>What other definition of infinite decimals do you think would also be valid?

An integer and a sequence of digits in [0, 9] with addition, multiplication, and order defined on them and with a equivalence relation modulating out ∀n,m∈ℕ ±n/10^m =eq ±(n/10^m)*0.999...

>> No.6823985

>>6823975
It's not in the construction of the reals. It's in the appendix, the decimal system.

Infinite decimals are defined as the limit of a sequence of finite decimals with the same n digits.

>> No.6823988

>>6823977
Actually if you go and use epsilon delta in limits you actually got yourself a proof there.

But yeah, saying the limit of that series is 1 is literally saying 0.9999 ... = 1 so you still have to prove that.

>> No.6823992

>>6823985
>Infinite decimals are defined as the limit of a sequence of finite decimals with the same n digits.

No, they are their own construction retard.