Question

Proof that 1 + 1 = 1

The number, 1, is used in the abstract mathematical world for modeling.
Consider the "hyperwebster dictionary"

Now consider the infinite collection of sequences A = {
(a,a,a,a,a...),(a,b,a,a,a,a...),(a,c,a,a,a...)...(a,z,a,a,a...)...(a,a,b,z...)...(a,z,z,...)...
(b,a,a,a,a...),(b,b,a,a,a...),(b,c,a,a,a...)...(b,z,a,a,a...),(b,z,z,z....),
(c,a,a,a,a...),(c,b,a,a,a...)...
...
(z,a,a,a,a..),(z,b,a,a,a....)...(z,z,z,z,z,z..)
}

Then take the first "row" of the collection out, name it B, so we have
B = {
(a,a,a,a,a....)...(a,z,z,z,z...),
(a,b,a,a,a...)...(a,b,b,...)...
(a,c,a...)...
...
(a,z,z,...)
}

Then if we remove first letter "a" from each sequence, we get the set
{
(a,a,a,a,a...),(a,b,a,a,a,a...),(a,c,a,a,a...)...(a,z,a,a,a...)...(a,a,b,z...)...(a,z,z,...)...
(b,a,a,a,a...),(b,b,a,a,a...),(b,c,a,a,a...)...(b,z,a,a,a...),(b,z,z,z....),
(c,a,a,a,a...),(c,b,a,a,a...)...
...
(z,a,a,a,a..),(z,b,a,a,a....)...(z,z,z,z,z,z..)
}
and denote it as C.

Notice A = C

We can do the same thing for B, but instead of taking the sequences starting with "a", we take the letters starting with "b", and "c", and "d"
Thus for all 26 sets, adding them equates to A, but all of them are equal to A.

A_n as the set of sequences of A that start with 'n'
Then
A_1 + A_2 +... + A_n = A_n
And they all equal to each other
so we can rewrite it as
26 A_n = A_n

Notice A_n is not empty, so A_n can't be 0.

Thus if we model this, 1 + 1 + 1 + 1 + 1... + 1 = 1
Then we can see, 1+1 = 1

This is just my interpretation of the banach-barski paradox xd

Answer 1

And 2 plus 2 is fish because if you turn the second 2 around and overlay them it makes a fish cx

Answer 2

1 plus 1 is also window by the way because put the 1s together and the equal and you get window x'D

Answer 3

guess what this is not funny at all.
I couldn't find the video that i really wanted to post
but I found another one which can aslo deliver the msg https://www.youtube.com/watch?v=iKcWu0tsiZM

Answer 4

Nnesha thank you SO MUCH for posting that video
That was so interesting

Answer 5

I swear to god. I HATE PROOFS

Answer 6

np. I'll post the other one later.. I don't have time rn to find iit.

Answer 7

In what base are you adding the 1's?

Answer 8

The 1s represent the sets, since the sets are all the same.

Answer 9

For example,
Let A,B,C be sets.
Given A + B = C
and A = B = C
then A + A = A

(A could be empty set here)

Answer 10

If the 1s represent sets then you should use set mathematics in your proof. Not pluses.

Answer 11

Just saying, you should have clarified from the beginning what the operation PLUS represents from the beginning before you stated your proof. That would have helped.

Answer 12

True, I did not do that.