1.0   Is a plane infinite or finite?

    The mathematician begins his presentation by claiming that a plane is infinite:

    “ plane: A flat surface that extends infinitely in any direction in three dimensions. A
       plane is represented by a closed four-sided figure.” [1]

    “ 2D space consists of a flat plane, extending in length and width indefinitely” [2]

    “It is difficult to draw planes, since the edges have to be drawn. When you see a picture that
    represents a plane, always remember that it actually has no edges, and it is infinitely large.” [3]

    “ A plane is a flat surface that extends without end in all directions... Intuitively, a plane
       may be visualized as a flat infinite sheet of paper.”  [4]
     
    These definitions and notions summarily violate Euclid's definition of the word figure:

    “ A figure is that which is contained by any boundary or boundaries.” (Bk. I, Def. 14) [5]

    Therefore, whatever these 'experts' are referring to is not a part of Geometry.  

    Nevertheless, I wonder what such a contraption as defined by the mathematicians might be used for. No
    one has ever seen or imagined an infinite plane, whatever that is. If you have, go ahead and draw one for
    me. I betcha anything you draw has boundaries! If the circle or the square were to be infinite, we would
    not be able to distinguish one from the other. How would we establish relations between these alleged
    figures? How are we supposed to visualize that a plane is 2-D if it cuts the Universe in half? How do you
    get to the other side of the plane if the plane is infinite? How can you discard the possibility that you are in
    fact sitting on a cube (Fig. 1)? How long should we watch this movie or how far should we travel before
    we can call it a plane?

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The edge of space?
Sure! Just beyond
Summum codum!

What does an
infinite triangle
look like
Adapted for the Internet from:

Why God Doesn't Exist

    As with most words used in Mathematical Physics, we can trace most of the problems with the word plane
    to faulty definitions. The word plane has its roots in the Latin planus, meaning flat, which in turn has more
    ancient origins. Hence, this word started out as an adjective. Unfortunately, the Greek geometers
    converted it into a noun. The word plane is a noun if it is a synonym of face, like the face of a cube, in
    which case it is definitely a finite object. It becomes an adjective when we use it in lieu of flat. (e.g., a plane
    triangle). The presenter is merely reconfirming that a triangle is flat. In this context, the word plane is
    redundant and unnecessary. The main point, however, is that the word flat does not mean infinite. There
    is yet a third possibility and that is when we use the word plane to designate a category of objects that are
    flat. As the heading of a category it is grammatically a noun, but what we are actually referring to is that a
    circle or a square belong to the category of ‘flats.’ Again, as a mere category (heading), the word plane
    cannot itself be qualified as infinite or finite. A circle is not infinite. It is just flat and rightfully belongs to the
    category of geometric figures known as planes. Hence, it makes no sense to qualify planes as infinite
    under any of its definitions, more so if we factor in that, like an edge, planes are not standalone objects
    (Fig. 2).
Whew! I'm pooped!
We've walked infinitely
today, Steve, and we still
see no boundary. I
guess that confirms our
hunch. Our world is flat
as a pancake!
No! It’s just
that we never
figured out
how you guys
manage to live
on your own.

    2.0   The words infinite and infinity are unscientific

    For the purposes of Science, an object is that which has shape. There is no such thing as an infinite
    geometric figure. Therefore, even as a category of geometric figures, the infamous mathematical plane
    cannot be infinite. An infinite object is a self-contradiction because it violates the definition of the word
    object, a word that happens to be a synonym of finite. The word object implies form, and we cannot talk
    about shape if the object extends 'infinitely.' To declare that an object is infinite is also irrational
    because the presenter is saying in a round about manner that he has yet to reach the end of the thing.
    How does he know that it is infinite? Perhaps he simply needs to walk a little further!

    The mathematician is actually saying that the carpet grows faster than he can make up the distance. But
    size is not a problem in Science. From God's perspective, everything has shape. The proponent merely
    needs to present a mockup of what he thinks the carpet looks like before he talks about the carpet, and
    hopefully, this means that the carpet has a contour. The mathematician is confusing proof (what he can
    verify or measure) with what is irrespective of observers. In Science, we don't need to walk to the end of
    the park to verify that it is indeed a rectangle. The park is a rectangle or not whether there is anyone on
    the planet to admire its beauty. A park is a rectangle by definition: because it belongs to a category of
    geometric figures that meets certain requirements. Nevertheless, a triangle has no dynamic properties.
    It may be flat, round, or made of so many lines or sides. None of these qualitative parameters require
    motion or measurement. The word infinite , instead, dares the juror to walk until he finds an edge to the
    figure. Therefore, the word infinite is unscientific and should be removed from the vocabulary of
    Science. There is no context in which anyone can use the word infinite consistently.


    3.0   Conclusions

    Whenever the mathematician says that a plane is infinite, he is not referring to the category called
    planes (I’ll again write it in plural form). He is referring to the hyperplane, an unfathomable 0-thickness
    sheet that divides the Universe in half.  The mathematical hyperplane is not a geometric figure. A
    hyperplane is an activity: cutting something in half. The mathematicians are confusing a cross-section
    of an object with the category of geometric figures known as planes. For the purposes of Science, a
    hyperplane or cross-section is not a plane. These definitions and notions cannot be used to designate
    geometric figures, which means, in turn, that such notion is divorced from Geometry.

Fig. 2

square joke
Fig. 1   The infinite plane