Thread 16737432

How do you prove that 1=1?

things being equal to themselves is a basic axiom from which that would follow.

>>16737432 (OP)
From the fact that 1=1, then you can replace one one (or even two ones) and solve it, wich also allows you to prove that 0=0 as an extra

>>16737441
>>16737443
idiots

>>16737432 (OP)
Via demonstration of no other possibility.This can be done analytically via definition. Assign some Px and then those define one.
Of course, all reasonably intelligent people know that one is the only number and the use of shorthand numbering schemes is projection.

>WTF is an axiom? I've never heard of that.
God we live in a gay age.

>>16737432 (OP)
do the calculation

>>16737432 (OP)
It's not self-evident that 1=1. Consider two coins that both indicate "1 moneys". It's not clear that both coins are equally valuable just because both coins make such statement. Both coins may be different in all sorts of ways that we may or may not consider significant and consequential for how we value these coins. So the statement 1=1 raises the question in what ways 1=1 and also the question how accurate the statement is. Because if 1=1 is not axiomatic then we need a reference, a comparison, perhaps even an observation of things to determine the statement to be true or false.

>>16737432 (OP)
it just is, okay

>>16737432 (OP)
Really? It’s just singulars. God damn it.

>>16737432 (OP)
By definition of 1.

>>16737432 (OP)
If 1 = 0.9999..., then 1 doesn't always = 1.

>>16737456
mega pseud

>>16737849
>It's not self-evident that 1=1.
yes it is. didn't even read the rest of your post. you're dumb.

The equals sign is two rotated 1's on top of each other. Simple as

>>16737432 (OP)
Start by assuming that 1 does not equal 1, which obviously isn't fucking true, so by way of contradiction 1 = 1.

What else would it be?

Assume for the sake of contradiction that 1 does not equal 1.

X - X = 0
Let x = 1
1 - 1 = 0
1 = 1
This contradicts our assumption that 1 does not equal zero. Therefore, 1 = 1.

>>16737432 (OP)
You don't prove it, you define what it means to be equal.

>>16737978
> 1 - 1 = 0 is assuming what we are trying to prove.
Lots of onaholes in this argument bud.

>>16738004
go look up what a proof of contradiction is retard.

>>16738010
why are we allowed to say 1 - 1 = 0 retard.
> wouldn't it just be "obvious" then that 1 = 1?

None of these are even "proofs" lol we are all bullshitting. I'm pretty sure the proof of this is not trivial and it is a few pages.

0 = 0
suc 0 = suc 0
1 = 1
QED

>>16738019
Saying 0 = 0 is true is the same thing as saying 1 = 1 is true, so this really doesn't do anything.

>>16738017
I don't know of any formal systems for logic that don't take reflexivity of equality as an axiom

>>16737432 (OP)
cite x=x for all x, the law of identity

>>16738015
because x - x = 0 retard.

>>16738151
fair enough, I guess i really didn't think of that, you are absolutely right. What was I thinking.

Read Atlas Shrugged.

>>16737432 (OP)
symmetry nigga

>>16738025
Nope, you need to assume 0=0 for literally any arithmetic to work, 1=1 on its own is useless, you need an identity

>>16737432 (OP)
>List of axioms:
>1. a=a
QED

>>16737849
If you have an american paper dollar and a canadian loonie, you would have an equal number of "money" in that you could seperate them into their own piles and number them and arrive at the same count despite having different values. The value is not the same as the count, which would be 1 by definition and thus is self evident.

>>16737432 (OP)
If anyone disagrees you simply beat them into submission. It is that simple.

>>16738551
No, that is not how 0 is defined, it is defined by the additive identity x=x+0 or >>16738151, so technically it is proving that 0={}.

>>16737432 (OP)
by twisting the nipples of the fucker that says to you "nuh uh, they are not" until he yields, it called proof by you either agree or i rip your nipples of and mount them to a plaque like a deer

>>16737432 (OP)
Take it as an axiom and don't think about it. That is just the definition of equality.

>>16737893
Anybody that writes 1 = 0.99999999.... was just to lazy to or couldn't use tilde equals.

>>16738742
What if you have one gold coin and another gold coin with its edges clipped?

>>16738972
No, they just know that .999... equals exactly 1 because they know 1/3 is exactly .333... so 3 times that amount is exactly 1.

>>16737432 (OP)
If I have one thing, then I will have one thing.

>>16738982
So if you have one apple tree seed, it can only ever result in one apple?

define equality of sets as follows:
X=Y∀x∈X (x∈Y)∧∀y∈Y (y∈X)
substitute X for Y in there and WA LA!

>>16738978
nah we know that due to abc*whatever*/*equal amount of the base minus 1*=0.abc*whatever*... for any base

>>16738004
it's not just 1-1=0
any number subtracted by itself is 0
5-5=0
x-x=0 etc
Also be nicer next time

>>16738989
>define equality of sets as follows
>X=Y∀x∈X (x∈Y)∧∀y∈Y (y∈X)
>X=Y
>=
anon...

>>16737916
lmaoooooo

>>16737444
>I don't know what axiomatic logic is

>>16739010
So what is .333... times 3?

…lol

>>16737432 (OP)
I went on paint and dragged the first 1 over the second one and it was completely identical
So yeah, it's the same

1=1
i just 1

>>16740919
No, 1 equals infinite things because x/x=1 for all x.

i'm interested in the formal proof but i think you can prove it with the number line by showing that any number which occupies the same space as another is equivalent to that number. hence 1=1 and 0.999.... (which is infinitely close to one, and is essentially a base-10 rendering of 3/3) =1.

>>16741497
By that definition 1 is not exactly equal to 1 it is just "infinitely close" to being equal to 1, whatever that means.

>>16739928
0.333... comes from 1/3 being the reduced form of 3/9, hence why the 3's repeat, so 0.3333...*3=1

>>16741497
0.aaa...(with a=(current base)-1) equals 1 for all bases

>>16737432 (OP)
[0.] 1=1 one equal one
[1.] 1 /= /1 one no equal no 1
[2.] 1 one
QED

>>16737432 (OP)
I will find 1 and create a sealed vacuum, then I will burn it an irradiate it, then freeze it and melt it, eventually I will look inside and of it multiplied and created life it wasn't 1

>>16739011
Any number minus itself is zero because every number is equal to itself. Saying that every number is equal to itself already presupposes that 1=1 so it doesn't work.

>>16741491
I press the 1 button on my keyboard, then I pressed the same button and it showed the same symbol
I am confident that they are the same

>>16737432 (OP)
Well, first, you sort of need to define 1. After that, it gets pretty easy really.

>>16741532
Which means .999...=1

>>16741674
>Any number minus itself is zero because every number is equal to itself
No, every number is equal to itself because any number minus itself is zero.

>>16737432 (OP)
Modern mathematics is a house of cards based on primitive finger counting.
It ignores physical reality and so instead constructs elaborate abstractions, which in turn lead to all sorts of absurdities.
Rather than accept that these absurdities indicate mathematics is based on flawed fundamentals the mathematicians paper over them with stacks of bandaid "fixes' which merely conceal the logical inconsistencies.

>>16737978
>X - X = 0
How do you prove X - X = 0?
Tardofuck

>>16742151
If you post x posts, then delete all x posts you posted, how many posts remain if not 0?

>>16742135
yeah

>69 posts, not mention of equivalence relation
the symbol "=" is used to denote set elements related by an equivalence relation, a type of relation (that is, a subset of a cartesian product between two sets. if (x,y) is an element of the relation, it is typically notated x R y which is read "x relates y")
an equivalence relation is defined on a set by 3 relation properties
1) reflexive (for all x, x R x)
2) symmetric (x R y implies y R x)
3) transitive (x R y and y R z implies x R z)
if you have a relation that satisfies these properties, then you have an equivalence relation, which partitions the set into equivalence classes, and have license to use the the symbol "=" in place of "R"
so 1 = 1 because you are implicitly invoking the notion of an equivalence relation by using the symbol "=", and equivalence relations satisfy reflexivity by axiom

>>16742580
That's just some formalism.

>>16742596
using "=" is just some formalism

One is One. Even a zero is a one in a state of absolute nothing. Holy shit.