/sci/ - Science & Math

Yes, proof not necessary

>every rational has a rational between them, so if a number is between two rationals it should be rational.

Sqrt 2 is between 1 and 2 so therefore sqrt 2 is rational

Op is retarded

>>15809566
>constructing sqrt(2) to indicate it's existence
even if you used contradiction it would still be construction because it's not defined.
>inb4 it exist because I said so aka LUB of R

I don't know about things like the know-it-all number, but constructive reals are obviously real and you probably have an implementation of them in your phone if you're not an iToddler.
https://cacm.acm.org/magazines/2017/8/219594-small-data-computing/fulltext
>also are imaginary numbers real?
>doubting the existence of ordered pairs

>>15809555
numbers (natural, real, complex, etc.) only have existence as ideas and not physical existence or embodiment in a meaningful way. at best, they summarize similarities between different arrangements of real things, but those summaries are just ideas produced by some intelligence.r0a2m

>>15809585
>>15809579
>it's all in my head because I'm such a schizo
wtf do newfags really believe this shit?

>>15809555
> I mean 0.999... clearly isn't 1

>>15809566
>affirming the consequent
this should be bannable tb h

>>15809630
Yes, 0.9999... isn't a number and in particular it's upper bound/limit is 1, but it is not 1 itself

>>15809555
There are lots of ways to demonstrate square root of two can't be a rational number. One I like is writing it as a continued fraction. After the first term it goes into a never ending cycle. All rationals have a finite representation as continued fractions.

>>15809555
Grab 3 apples. Boom number 3 is real. Now grab an imaginary number of apples.

>>15809662
Wrong.
0.999... is 1.
0.111... in base 2 is also 1.
If they are not 1 then it exists a number between them and 1. Show me that number.

>>15809673
>0.999... is 1.
What is 10-9?
What is 1-.9?
What is 10-.9?
~1-.99
Ect etc
1-.9999....

>>15809673
0.999... index n
< 0.999... index n+1
now fuck off already, stop abusing notation
yes the limit of the sum of 9/10^n is 1, but 0.999... index n is not 1.
Natural are not bounded above btw

>>15809673
Pretty bad proof.
For example I could easily redefine infinite decimals so that
.999... = {.9, .99, .999, ... | 1.0, 1.00, 1.000, ...} = [math]1 - \frac{1}{\omega}[/math].
Then .999... would be a number less than 1, albeit not a real number,
and a number between .999... and 1 would be [math]1 - \frac{1}{2\omega}[/math].
It doesn't have an infinite decimal representation, but it's still a number.
Granted wanting to have infinite decimal representations for every number in your set is one reason for constructing the reals without nonzero infinitesimals, but if you want to say that you should say it explicitly.

>>15809555
> 0.999... clearly isn't 1
That requires the concept of the infinitesimal digit. That is the the less significant digit after an infinite sequence of digits. Without that the difference between 1 and 0.999... is an infinite sequence of zeroes, therefore zero, therefore both are the same.

>>15809607
Imagine not having numbers in your head.

>>15809671
that just implies that 3 exists due to platonism.
sqrt2 apples does not exist
also uncountably infinite isn't real btw

>>15809666
>writing it as a continued fraction
>writing it as a rational
cool beans

>>15809692
is this (You)? >>15809563
you're a schizo, you need to take your meds.
magic unicorns are real too right?

>>15809693
>sqrt2 apples does not exist
How do you know? Have you tried?

>>15809698
>is this (You)?
No.
>magic unicorns are real too right?
Magic squares are.

>>15809688
0.AAA… in base 11 is between 1 and 0.999… in base 10.

>>15809555
>and every rational has a rational between them, so if a number is between two rationals it should be rational.
every person has a parent who is older them them, so if a person is older than you he must be your parent

>>15809555
Given the unreasonable effectiveness of mathematics I'm gonna go with yes. Either that or god exists and he likes fucking with us

>>15809555
>Are real numbers real? also are imaginary numbers real?
depends on what you mean by real. you can't show me -1 apples nor 1.5 apples (you can just as easily define 1/2 of an apple as 1 new thing separate from a whole apple for example) but that doesn't make those numbers any less significant to how we use those definitions in life.

>I mean 0.999... clearly isn't 1
add 0.111.. to 0.999..

>and every rational has a rational between them, so if a number is between two rationals it should be rational.
??? i dont understand this question

>>15809912
false equivalency

>>15809941
>Either that or god exists and he likes fucking with us
>both are true
it's over for us math bros... we're being punished for not just farming and having babies
IT'S NOT MY FAULT DO YOU KNOW HOW EXPENSIVE LAND IS THESE DAYS?!

>>15809555
Good video on the subject.
https://youtu.be/CTpp0EChDbI?si=w89K3RbvYPksBM9P

>>15809693
>sqrt2 apples does not exist
don't mind me arranging these 16 apples in a square and count rows

>>15810982
That retard only has at most 10 fingers, tell him to arrange 9 apples in a square.

>>15809555
>only integers exist
>irrational numbers are a hallucination
>pi doesn’t exist
>there’s no such thing as a circle
I mean this unironically
>t. knower

>>15811533
based

>>15809555
no number is "real", are you a retard?

This thread is the encapsulation of /sci/. Just pseudointellectual wanking of the same brainlets who post in every IQ and not-so-thinly-veiled pol thread.