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Topic: A toy conjecture which may lead to an other breakthrough conjecture - help request
Replies: 9   Last Post: Sep 8, 2013 4:10 AM

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William Elliot

Posts: 2,637
Registered: 1/8/12
About binary relations and their composition
Posted: Sep 6, 2013 10:58 PM
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> Let A be a set.
> Let pi_0, pi_1 be projections from AxA.
> Let F_0, F_1, G_0, G_1 be binary relations on A.

> Let phi_A be the maximal binary relation in (AxA) x (AxA) such that
> pi_0 o phi_A subset F_0 o pi_0 and pi_1 o phi_A subset F_1 o pi_1.

I don't see how pi_0 and phi_A can compose as
pi_0 subset AxA x A and phi_A subset AxA x AxA.

> Let phi_B be the maximal binary relation in (Ax
> A)x(Ax A) such that pi_0 o phi_B subset
> G_0 o pi_0 and pi_1 o phi_B subset G_1 o pi_1.

> Prove (or disprove) that Sigma=phi_B o phi_A is the maximal
> binary relation on A such that pi_0 o Sigma subset G_0 o
> F_0 o pi_0 and pi_1 o Sigm asubset G_1 o F_1 o pi_1.

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