6

Let Then x cannot we cannot have at once

x=f x=v

because f and v are different numbers.
The equation

(x-f)(x-v)=0

will denote that x=f or x=v that is that every
object chosen is either x or not-x. The idea is
that for each object chosen this holds so that
For each x=f that is that object is not x or x=v that
is that object is v.

Then (x-f)(y-v)=0

means each object chosen is either not-x or is y.
Cayley proposes to write the negative of this thus

(x-f)(y-v)≠0

but this would be the object chosen cannot be not x must be x and can't be
(nor) y. This states too much. The true denial of the first
equation would be (x-f)(y-v) is not always 0, not is never zero.
I have myself proposed (Logic of Rel p 7) to write
x>y to mean x's comprise some objects besides y's but
properly this can only mean x=v y=f (if v>f) and so is
? bad as equivalent to Cayley's proposal

Let Then x cannot we cannot have at one

x=f x=v

because f and v are different numbers.
The equation

(x-f)(x-v)=0

will denote that x=f or x=v that is that every
object chosen is either x or not-x. The idea is
that for each object chosen this holds so that
For each x=f that is that object is not x or x=v that
is that object is v.

Then (x-f)(y-v)=0

means each object chosen is either not-x or is y.
Cayley proposes to write the negative of this thus

(x-f)(y-v)≠0

but this would be the object chosen cannot be not x must be x and can't be
(nor) y. This states too much. The true denial of the first
equation would be (x-f)(y-v) is not always 0, not is never zero.
I have myself proposed (Logic of Rel p 7) to write
x>y to mean x's comprise some objects besides y's but
properly this can only mean x=v y=f (if v>f) and so is
? bad as equivalent to Cayley's proposal