Law of identity

[ohkarmahd]

(0=0)=(1=1)

0=1

doesn't 0=0 reduce to 1 because of double negation? like saying nothing is nothing

(A=A) = (-A=-A) reduces to A=A though, how does it reduce to A=-A?

it reduces to A=A like this:

(A=A) reduces to A
(-A=-A) reduces to A
So A=A?

-A=-A and A=A would be the same thing

[alan1000]

The Law of Identity does not enter into arithmetic; so, 0=0 and 1=1 merely state the obvious. But in no sense is 0=0 equivalent to 1=1, except in logical form, because 0 and 1 are different values.

The proposition (0=0)=1 has no intelligible meaning.

[alan1000]

Perhaps my first thought was a little terse.

The proposition (0=0)=1 "reduces" to the proposition 0=1, which is obviously incorrect. Are you perhaps confusing the statement of equivalence with the operation of division? Eg 2÷2=1.

[ohhkarmahd]

The Law of Identity does not enter into arithmetic; so, 0=0 and 1=1 merely state the obvious. But in no sense is 0=0 equivalent to 1=1, except in logical form, because 0 and 1 are different values.

The proposition (0=0)=1 has no intelligible meaning.

0=0 is like saying 0 isn't equal to not-0, which is like saying not-0 is equal to not-0, which is like 1=1, because 1 isn't equal to 0 or 1 is equal to not-0, as you affirm. so 0=0 is like saying 1=1. So that makes you wrong?