Re: Is one-to-one mapping valid for comparing infinite-sized sets?

On Sep 20, 2:56 am, Virgil <Vir...@xxxxxxxxx> wrote:
"If the extent around points were ever filled,
 then some points in R would be adjacent."

Is that true according to you?

Yes, if "filled" means "filled by points".

Do you mean that the midpoint between two points need not always be a
point?

No. I don't mean it. You can always identify more points anywhere
inside an extent.


Since the extent around a point is always
unfilled, then ... what could come next?

Its the extent !!! right next to every point.

What comes next AFTER that extent? The same extent again, repeating
itself endlessly? That is what you seem to be saying.

No. Whenever you imagine or identify a point, you are creating one
more new extents around it.

Just how far does one of your alleged 'extents' extend?

If that distance is greater than zero, there is another point within
that same extent. if the distance is not greater than zero, then your
alleged 'extents' do not extend at all.

The magnitude of an extent is always greater than zero. That is the
essence of an extent. Yes, you can imagine any more points inside it,
possibly breaking the extent into more extents.
.

Relevant Pages

  • Re: Is one-to-one mapping valid for comparing infinite-sized sets?
    ... In what directionfrom the point does an extent extend? ... If that distance is greater than zero, ... Is there any mathematical task that cannot be as easily completed ...
    (sci.math)
  • Re: [PATCHv3 0/4] sys_indirect system call
    ... This no system call allows us to extend existing system call ... It seems to me that we could accomplish the same thing by passing the number of parameters in the upper bits of the system call number register If set to zero, we'd fill in the legacy number of registers Unspecified arguments are then forced to zero before invoking the target function; we could also make a register count available if need be. ... Alternatively, the same thing can be done with a dense system call number space by adding a number of parameters field to the system call table, however, that is more invasive in that one has to poke something into each architecture (unfortunately -- it would be so much nicer if there was a central metafile which one could process into the various architecture system call tables.) ...
    (Linux-Kernel)
  • Re: Is one-to-one mapping valid for comparing infinite-sized sets?
    ... process only the usual math discussion. ... Just how far does one of your alleged 'extents' extend? ... If that distance is greater than zero, ...
    (sci.math)
  • Re: Measurable functions and measure zero
    ... Pawel Gladki escreveu: ... function f except at the points of set E of measure zero. ... is measurable no matter how we extend f. ...
    (sci.math)
  • Re: sockets affected by IPsec always block (2.6.23)
    ... We made an explicit decision not to do things this way. ... If xfrm_larval_drop is zero, ... non-blocking semantics do not extend to IPSEC route resolution, ...
    (Linux-Kernel)
Quantcast