/sci/ - Science & Math » Thread #12446259

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Anonymous Thu 10 Dec 05:26:47 2020 No.12446259 View Reply Original Report

Quoted By: >>12446272 >>12446597 >>12448195 >>12450203

Prove

$\left \lfloor \lfloor{x}\right \rfloor \rfloor = \lfloor x \rfloor$

Anonymous

Anonymous Thu 10 Dec 2020 05:29:55 No.12446272 Report

Quoted By:

>>12446259
x=x
qed

Anonymous

Anonymous Thu 10 Dec 2020 05:33:00 No.12446288 Report

Quoted By:

$\lfloor \lfloor ... \lfloor_n x \rfloor_n ... \rfloor \rfloor = \lfloor x \rfloor$

Anonymous

Anonymous Thu 10 Dec 2020 05:34:10 No.12446295 Report

Quoted By: >>12449814

floor(z) = z, if z is an integer
floor(x) is an integer

follows that
floor(floor(x)) = floor(x)

Anonymous

Anonymous Thu 10 Dec 2020 06:53:27 No.12446597 Report

Quoted By: >>12449814

>>12446259
Let $a = \lfloor x\rfloor$ . Then $a \in \mathbb{Z}$ . Recall that for all $b \in \mathbb{Z}$ , $\lfloor b\rfloor = b$ . Therefore $\lfloor\lfloor x\rfloor\rfloor = \lfloor a \rfloor = a = \lfloor x\rfloor$
QED

Anonymous

Anonymous Thu 10 Dec 2020 16:11:01 No.12448195 Report

Quoted By: >>12448235

>>12446259
It's axiom, but

But left right - right side = empty set, therefore they are equal.

Anonymous

Anonymous Thu 10 Dec 2020 16:23:14 No.12448235 Report

Quoted By: >>12448551

>>12448195
this has to be the lowest iq post I've ever seen on /sci/.

Anonymous

Anonymous Thu 10 Dec 2020 17:49:48 No.12448551 Report

Quoted By:

>>12448235
signed integer overflow IQ

no, really, it's extended definition of equivalence, it's good to have as macro if you crawl trough equations, because you can just replace left and rights and stack divide get one somewhere and start again

Anonymous

Anonymous Thu 10 Dec 2020 21:46:35 No.12449814 Report

Quoted By:

>>12446295
good
>>12446597
better

Anonymous

Anonymous Thu 10 Dec 2020 23:14:01 No.12450203 Report

Quoted By:

>>12446259
define floor x

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