prove to me that a = a

>>9163021
if you reply to this thread make sure to put "sage" into the options section thanks

The = relation is reflexive. Q.E.D.

that's a self evident axiom you stupid fuck,
means already proven.

rephrase your question as "prove to me that a = a may be false"

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>>9163021

>>9163110
quantum electrodynamics?

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>>9163021
There is only 27 letters, so if:
a != b
a != c
a != d
a != e
a != f
a != g
a != h
a != i
a != j
a != k
a != l
a != m
a != n
a != o
a != p
a != q
a != r
a != s
a != u
a != v
a != w
a != x
a != y
a != z

Then:
a == a

xD

>>9163021
Prove to me that:
> u != fag

>>9163021
theorem: a = a.

proof: think about it

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>>9163401
>there is only 27 letters

Which impoverished nation do you come from?

>>9163401
>>9163405
loled, 26* and I forgot "a != t"
cancer

>>9163021
You can prove it using set theory.
I'm to tired to write it out, so you can read about it on your own time.

reflexive axiom of equivalence relations
its that fucking simple

>>9163021
What's a? and what's =?

>>9163356
Quod erat demonstrandum
Means the mathematical proof is complete.

>>9163021
https://en.wikipedia.org/wiki/Law_of_identity

>>9163021
>Prove that a thing is that thing

>>9163021
Prove that what equals what now?

>>9163485
I remember in my Discrete Structures class the teacher always reminded us to explicitly state was something is. So for example i might say, "Assume A is a set". The a=a question would have triggered him lol.

>>9163021
by definition of =

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>>9163164
axiom does NOT mean already proven, it means that it's unprovable

None of yall have valid proofs
And to those people saying "le transitive property lmao" THEN PROVE IT YOU CANT JUST SAY IT YOU BRAINLETS

>>9163021
= is reflexive by definition

one can only prove it to themself
give up naow

>>9165516
If you're wondering how, touch your skin at a certain point the remove a slice of skin and touch where the skin was, then look at an object, it is not another.

a cannot be a for no two things can possibly share the exact same properties

for example, two identical clones have different gps values

>>9163401
You better have written a program to print that out

>>9163021
Define "a = a"

>>9163021
a^2 = a * a
(a^2)/a = a
(a * a)/a = a
a/a * a = a
1 * a = a
∴ a = a

a=a Reflexive property of equality QED

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from Bourbaki - Set theory

>>9163404
>proof: left as a problem for the reader

>>9163021
We first assume that a may = !a
if (a = !a), (a = !a) = (a = !a)
else (a != !a) = (a != !a)

>>9165513
>"Transitive" property
>why don't you prove an axiom lol
B r a I n l e t.

>>9163021
Why should I bother proving that when it is self evident? There are far, far more interesting things to prove.