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How do I write the square root of 2 as a...
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You are currently reading a thread in /sci/ - Science & Math

How do I write the square root of 2 as a fraction? And don't tell me I can't.
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7/2

it's right there in the symbol retard
>>
root(2) / 1
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>>7805380
This
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>>7805363
I know it's bait but for anyone who wants to understand the troll here you go.
https://en.wikipedia.org/wiki/Square_root_of_2#Proofs_of_irrationality
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>>7805367
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>>7805363
here i wrote a proof for you
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>>7805383
>>7805390
Irrational numbers disturb me.
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>>7805411

Don't worry, they can be quite fun.

Have you been introduced to complex numbers? they make irrational numbers a lot easier to manage.
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>>7805363
you can write it as a fraction with infinite digits though.
141421356237.../100000000000...
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>>7805463
Nice.

This also means the numerator of that fraction also an infinite digit prime right?
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>>7805390
There's no contradiction because you did not assume that a and b were in lowest terms.
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>>7805470
There's no such thing as an infinite digit prime.
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>>7805479
Once you can no longer reduce a/b you will have an odd numerator or denominator which contradicts the fact that both must be even.
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>>7805470
I suppose so, it probably has to be prime.
>guys, we found a prime that has infinite digits, what do we win?
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>>7805470
>>7805492
No, because even if "infinite digit prime" made sense, there's no reason why

141421356237.../100000000000...

can't be reducible, because reducing it still leaves you with nonfinite numerator and denominator.
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>>7805485
well if we are allowed to define an infinite digit number, why cant some of them be prime?
100000000000... wouldnt be prime.
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>>7805418
How can complex numbers make rationals less disturbing
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>>7805463
No, just means it isn't divisible by 2 or 5, go be an irreducible fraction, could still be divisible by 3 or something.
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10000/7069

there you go, anon
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>>7805505
Why *can* it be prime? Look up what prime means and then get back to me.
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>>7805509
Why couldn't it be divisible by 2 or 5? Reduce it by 2 and you get

7071067811865... / 500000000...

Changes nothing because you will never reduce it to a finite rational.
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>>7805363
1+1/(2+1/(2+1/(2+1/(2+...
>>
Can't you just measure the line with a ruler?
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>>7805540
Math isn't restricted by reality, we would still have to go past the plank length.
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>>7805569
arent rulers just short planks?
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>>7805363

Like this:

pastebin.com/GsJYCgHc
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>>7805512
Division is closed over R, a number in R need not have a finite amount of digits. The definition of prime is that the number is only divisible by 1 and itself. There are an infinite amount of prime numbers. Therefore, there must be prime numbers with infinite digits.

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>>7805584
Yes, but but irrational numbers are hard to reason with.
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>>7805505
>well if we are allowed to define an infinite digit number
If by "number" you mean "integer," this is not something you can define.
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>>7805591
>There are an infinite amount of prime numbers. Therefore, there must be prime numbers with infinite digits.
There are an infinite number of primes. Therefore one must be divisible by 4. You see why this line of reasoning is fucking incorrect, right?
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>>7805380
Or 2/root(2)
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>>7805630
That is not a proof that there cannot be infinite digit primes.
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>>7805525
nice, it does equal 2^0.5
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>>7805411
It's okay Pythagoras.
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>>7805651
First of all, digits have nothing to do with a number. Second of all, an integer with infinitely many digits isn't well defined -- if x has infinitely many digits, what is x-1? What about x^2?

It's not a proof, no. But I hoped it would show you just how stupid you are.
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>>7805380
>>7805632
$\displaystyle \frac{2}{ \sqrt{2}}$
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99/70, CS students use this fact as a test to check if their software computes roots properly
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divided by
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>>7806914

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>>7806918
>>
>>7806934

Shit's exact.
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>>7805507
By providing a scapegoat.
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>>7805390
If a^2 is even and a^2/b^2i is even that doesn't mean b^2 has to be even.
6^2/3^2=2^2
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>>7805363
You could write a computer program that makes a convergent fraction. In pseudocode:
x = 1, y = 1,
if (y/x > pi) then x = x+1
else y = y+1
print(x, y)
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Easy: Sqrt(2)/1
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1/1 in base root 2
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type (x)
replace (x) with ((x)+2/(x))/2 10 times
replace (x) with 1
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Make taylor series of sqrt(x) at 2, evaluate, represent as a fraction of infinite sum(s).
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>>7805491
>>
>>7805667
I chuckled
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>>7805507
because they let you solve roots of negative numbers
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>>7805363

Here you go: pastebin.com/XJB078AK
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>>7805630
this
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>>7805683
There is prime with infinite number of digits.
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>>7807047
>not vi
Please tell me you're not serious.
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>>7805525
This.

$\displaystyle \sqrt{2} = 1 + \frac{1}{2+\frac{1}{2+\frac{1}{2+\ldots}}}$
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>>7808584
why didn't it work.
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>>7805363
go away pythagors
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>>7808095
Sure, in a nonstandard number of arithmetic, there is a hyperfinite prime.

See: https://en.wikipedia.org/wiki/Hyperinteger
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>>7805591
>Division is closed over R, a number in R need not have a finite amount of digits.
Technically true, but irrelevant to what we're talking about. 141421356237... and 100000000000... are not real numbers.

>There are an infinite amount of prime numbers. Therefore, there must be prime numbers with infinite digits.
No, all primes have a finite amount of digits and there are an infinite amount of pimes.
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>>7806993
Ah but a^2/b^2 is not just even, it is equal to 2. This must mean b^2 is even since a must be an even integer for a^2 to be even.

a^2/b^2 = 2
(2n)^2/b^2 = 2
b^2 = 2n^2
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>>7808598
Yes they are, and 141421356237... minus 100000000000... is 41421356237...
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>>7806914
>>7806918
exact as fuck m8
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2/sqrt(2)
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>>7808630
No, they're not. Look up how reals are defined. What you are talking about is just a badly written hyperreal
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>>7808662
I wasn't the original guy. I was trying to satire him, make a joke, since the funny part about subtracting "numbers" like that is that the result is ostensibly bigger than either.
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>>7805363

Why don't you go play some gay music, Pythagoras.
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>>7808625
I get it, thanks.