/sci/ - Science & Math

e rounds to 2.72
pi rounds to 3.14

counterexample.jpg

>yfw

no, OP, they both round to 0

>mfw everything is 0 when rounded to 0 significant figures

>>3104833
And a wild corollary appears.

>yfw your calculator's rounding disproves Fermat's last theorem:

1782^12 + 1841^12 = 1922^12

>>3106701
>http://www.google.co.uk/search?q=(1782^12+%2B+1841^12)^(1%2F12)
>mfw google calculator does the same
>mfw I have no face

>>3106692
I would like to believe this forum isn't dumb enough to fall for this, but you never know.

>>3106710
Thought I would throw it out there before casually reeling a few tards / angry wannabe intellectuals in.

>>3106710
>>3106720
where's it wrong then?

>>3106722
They aren't equal, the numbers are just so large that rounding in standard form makes them round to the same thing. You can tell it wouldn't work by looking at which numbers are odd and even, doesn't follow through.

>>3106732

I think they're talking about >>3106692

>>3106743
yep

>>3106722
Complex log is multi valued.

>>3106750
>>3106722
e^x is one-one only when x is real

equating arguments of functions with equal values isn't allowed when functions are not one-one, as when x is complex in the exponential function.

>>3106762
In before me. This, basically.

>>3106762
>>3106758

oh, of course

>>3106692
fuckin hilarious "equate indices"

im gonna start using "equate indices" on tests.

<span class="math">e^{3i\pi} = -1 = e^{i\pi} [/spoiler]

<span class="math">3\pi [/spoiler]is equivilent to a rotation of \pi

>>3106692

This is saying <span class="math"> ln(3i\pi) = ln(i\pi) [/spoiler]

complex log is multi-valued, that's all.

>>3106877
>>3106900
What? This is a legitimate step with real numbers, only wrong here
.

>>3106916
no it aint

> this is my face upon hearing all you fucking idiots with your "complex log is multivalued" bull shit

>>3106921
Trolling?

Er, yeah it is. If 2^x=2^3, x=3

>>3106923
> math, one example proves the general case
> this thread
> dont want to live on this planet anymore

>>3106923
16/64 = 1/4. This does not mean you can cancel the sixes as a legitimate step.

>>3106925
For any real number, if a^x=a^y, x=y, obviously always.

>>3106932
are you fucking kidding me

> Prove the theorem by "obviously always"
> WAT

>>3106941
Give a counter example.

>>3106953
>>3106953

i've got a good one:


e^(i*pi) = e^(3*i*pi)

lrn2complexnumbersashole

>>3106969
Lrn2readmypost
>>3106916
"real numbers"

You so mad.

>>3106973

oh yeah,

well then what the fuck is the problem?
that's correct

>>3106983
People were implying equating indices is never a legitimate step. Was never a fucking problem with me, lol.

>>3106985

as long as domain is real numbers, that's perfectly legitimate.

a^x = a^y
take log base a of both sides,
since log is single-valued for real arguments:
x = y

same thing as equating indices.

c'mon sci...

>>3106932
a = 1
a^0 = a^1
now what?

>>3106994
First time I come here, people are questioning whether equating indices is legitimate. Not exactly impressed.

>>3107002

sigh, okay he's technically right. we have to exclude some special case(s?)

but in general, it's gorram right. jesus, sci. jesus

<span class="math">\mathbb{theremb}[/spoiler]: <span class="math">equating[/spoiler] <span class="math">indices[/spoiler]: proof, obviously always a^x=a^y implies x=y. QED.

>>3107012
What is your proof that 1+1+2 then? Some stuff does not need proving, it's a fact, not a theorem.

>>3107020
> What is your proof that 1+1+2 then?

>>3107012
> implying everything needs proving

>>3107025
Look, typing is a technical fucking skill okay?

What is your proof that 1=1=2, asshat.

>>3107030
For fucks sake, I shock myself.

1+1=2

>>3107030
it's not funny the second time

>>3107020
>>3107030
you must be fucking kidding me

>>3107033
I laughed at myself because it genuinely wasn't intentional either time. Anyway, answer the original post.

Stupidest thread on /sci/ at the moment. What is wrong with you people?

ITT drooling retards try to convince each other that "equate indices" is a valid mathematical operation, and try to prove 1+1=2.

>>3106922
y u mad tho? seriously.

<span class="math">0^{3}= 0^{53}[/spoiler]

>>3107042

agree

>>3107041
>>3107042
I'm finding it pretty fucking funny actually.

>>3107043
People actually mean it when they say stuff like "complex log is multivalued", it just demonstrates a huge misunderstanding.. The fact that people can get to that level and still have no clue, it's upsetting.

>>3107020
Aside from the obvious typo, this post still stands.

Wait is it not possible to prove 1+1=2? or does nobody know how or what?

>>3107050
That's depressing. What am I misunderstanding? Honestly it's a while since I really thought about this properly. Not a mathmo, physicist here.

>>3106922
But the complex logarithm is multivalued

>>3107057
It has never been proven, only proposed and attempted. Anyone trying to prove it in this thread is a huge retard and needs to stop missing his highschool precalc class.

>>3107063
has never read russell and whitehead's principia mathematica

>>3107061
>>3107062
Fuck this thread. I'm out. FUCK.

>>3107063
The proof:

Count one marble. Count another marble. Push them together. Two marbles.

Now kill yourself for needing a proof.

>>3107075
thats not aproof ...

>>3107083
It is. Is there any conceivable way that you could push two marbles together and get any other number than two? It is true by definition.

You do not need to prove something if any alternative is logically impossible.

>>3107070
<div class="math"> \ln[ \exp(i\theta)] = \ln[ \exp(i\theta + 2n\pi i) ]= \ln[ \exp(i\theta)] + 2n\pi i </div>

If a function is periodic its inverse has to be multivalued. What's the problem?

>>3107089
>true by definition.

Nope, 1+1=2 is called a postulate and cannot be proved, it is something you will just have to accept.

>>3107114
God, somebody present a proof using peano axioms to the genius ?

>>3107114
trying to turn math into religion

>>3107069
has never read Godel

>>3107069
>>3107125
Has never read Simulation and Simulacra

>>3107122

Learn about Euclids Postulates...

>>3107122
Uncomfortable with the similarities at base?

>>3107114
No.

Fuck you.

1 + 1 = 10

BITCH

>>3107118
>>3107114

>cannot be proved

Go fuck yourself.

The proof starts from the Peano Postulates, which define the natural
numbers N. N is the smallest set satisfying these postulates:

P1. 1 is in N.
P2. If x is in N, then its "successor" x' is in N.
P3. There is no x such that x' = 1.
P4. If x isn't 1, then there is a y in N such that y' = x.
P5. If S is a subset of N, 1 is in S, and the implication
(x in S => x' in S) holds, then S = N.

Then you have to define addition recursively:
Def: Let a and b be in N. If b = 1, then define a + b = a'
(using P1 and P2). If b isn't 1, then let c' = b, with c in N
(using P4), and define a + b = (a + c)'.

Then you have to define 2:
Def: 2 = 1'

2 is in N by P1, P2, and the definition of 2.

Theorem: 1 + 1 = 2

Proof: Use the first part of the definition of + with a = b = 1.
Then 1 + 1 = 1' = 2 Q.E.D.

Note: There is an alternate formulation of the Peano Postulates which
replaces 1 with 0 in P1, P3, P4, and P5. Then you have to change the
definition of addition to this:
Def: Let a and b be in N. If b = 0, then define a + b = a.
If b isn't 0, then let c' = b, with c in N, and define
a + b = (a + c)'.

You also have to define 1 = 0', and 2 = 1'. Then the proof of the
Theorem above is a little different:

Proof: Use the second part of the definition of + first:
1 + 1 = (1 + 0)'
Now use the first part of the definition of + on the sum in
parentheses: 1 + 1 = (1)' = 1' = 2 Q.E.D.

>>3107151
tl;dr

can't actually prove it though.

>>3107144
>>3107144
I lol'd

>>3107151
Ah, but can you prove the peano postulates though?

>>3107151
I reject P5. Do it without P5.

>>3107175
Back in my days the word "axiom" actually meant something.

>>3107175
>>3107175
>>3107175
> prove axioms

>>3107188
>>3107192
Exactly, I win. 1+1=2 is an axiom of modern mathematics, and needs no proof.

>>3107114
1+1=2 is (pretty much) definition of 2.
It just so happens that instead of S(0) we are used to write 1, and instead of S(S(0)) we use 2. It's just a little shorter that way.

Then using just two Peano axioms:
1) x+S(y)=S(x+y)
and
2) x+0=x
we get
1+1=S(0)+S(0)=S(S(0)+0)=S(S(0))=2

>>3107198

Finally someone sees the light...

1+1=2 isn't an axiom you retard

>>3107218
http://en(DOT)wikipedia.org/wiki/Axiom

You seem a little mad.

>>3107224
http://www2.wolframalpha.com/input/?i=axioms+of+mathematics

No, U MAD

>>3107229
http://dictionary(DOT)reference.com/browse/axiom

>>3107234
http://thesaurus.com/browse/postulate

>>3107247
http://en(DOT)wikipedia.org/wiki/Down_syndrome

>>3107247
http://en(DOT)wikipedia.org/wiki/Axiom_(disambiguation)