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?

[alan1000]

As you wish.

[Magnus Anderson]

doesn't 0=0 reduce to 1

It does not reduce to anything. That's merely Eodnhoj7 being Eodnhoj7.

One should keep in mind there are too many illogical people on this subforum. Yes, it's ironic but that's how it is.

[godelian]

(0=0)=(1=1)

0=1

"0=0" reduces to "true". It's a boolean type. So, the result is ,"true=true" which reduces to "true".

Some systems represent (false,true) as (0,1) but that is not a fundamental equivalence. It's just a possible implementation choice. In that context, "0=0" actually reduces to "1", i e. "true".

[Fairy]

(0=0)=(1=1)

0=1

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

Yes, it's a double negative.

[godelian]

(0=0)=(1=1)

0=1

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

Yes, it's a double negative.

That is not how any standard programming language would interpret it:

https://www.programiz.com/javascript/online-compiler/

console.log((0==0)==(1==1))

node /tmp/EszBAmDg39.js

true

Note that JavaScript distinguishes between the assignment "=" and the equality "==" operators.

It is not an arithmetic expression but a boolean one:

console.log(typeof((0==0)==(1==1)))

node /tmp/2FXaojIoxy.js

boolean

Therefore, the confusion is the result of failing to distinguish between the arithmetic and boolean data types.

If in doubt, use any compiler or script engine to check it. Not one programming language would implement this incorrectly.

[Eodnhoj7]

Proof by quantification allows 1=0:

There is 1 totality, as there is only all.

This totality is without compare otherwise it would not be the totality.

Without comparison the totality is indistinct.

As indistinct it is not a thing, it is nothing, thus 0.

Quantifying the totality results in the paradox of 1=0.

[Eodnhoj7]

doesn't 0=0 reduce to 1

It does not reduce to anything. That's merely Eodnhoj7 being Eodnhoj7.

One should keep in mind there are too many illogical people on this subforum. Yes, it's ironic but that's how it is.

The self evident nature of the laws of logic makes the axioms subjective. Agreed axioms are merely consensus and as consensus oriented are probabilistic as they are ratios within conceptions of truths between groups.