Using Huo Jian
Hua's Definition of Boundedness / 使用霍建華〈有界的定義〉
A revelation photograph of The Honorable Grandmaster Ji-Gong standing among
the Alishan clouds.
Background(摘要及背景)
Why prove ∃∞∀∞? One
of the reasons is to answer the demands to prove ∃∞∀∞. Otherwise students might be
throwing the raw whole eggs at schoolteachers on TV news, college students
might be shouting prove it! at professors publicly or in their offices, or
worse yet, an explicitly guaranteed explicit U.S. federal contract has
been breached by the assassination on the contract officers, `because
Grandmaster (霍建華 Huo JianHua in
a cosplay) has guaranteed us' to prove that infinity is not
infinity. `All serious, we're all serious'", or
etc,
so this paper proves that infinity is not infinity which re-evokes the default contract 默認替代. Besides
to prove that infinity is not infinity, this paper also proves ∃∞∀∞, and ∃unbounded∀unbounded, and ∃...etc∀...etc.
The writer (an
actual human person, not an AI) has used 霍建華
(Huo Jian Hua's) Definition
of Boundedness to prove that infinity is not infinity in this paper. Since the
paper has used Huo Jian Huas Definition of Boundedness, per guaranteed terms
of use on Huo Jian Huas Definition of Boundedness (The terms of use
for Huo Jian Huas Definition of Boundedness is described in the Guaranteed
Contractual Terms of Use for Huo Jian Huas Definition of
Boundedness paragraph under Prove That Infinity is Not Infinity section of
this paper), now it is your turn to honor the guaranteed contract rights-benefits to 霍建華
(Huo Jian Hua) all the way to the end, for
everybody has been all serious because Grandmaster's guaranteed us.
Abstract
The
infinity, denoted by ∞, refers to the infinity
from the infinity is unbounded axiom in this paper. Although the existence of
infinity has been debated for ages, infinity is unbounded axiom is our base
written reference for the infinity in this paper because "infinity is
unbounded" is an established axiom by consensus, guarantees, and supports, along
with the very important Definition of Boundedness from Huo Jian Hua to prove
that infinity is not infinity ∀infinity (IINI∀I theorem) as
guaranteed to be proved by The Grandmaster Ji-Gong (Huo Jian Hua in cosplay). Further,
IINI∀I theorem is the cornerstone in the Definition of Existence proof,
so Huo Jian Huas Definition of Boundedness is the key for the Definition of
Existence proof. Then, a whole class of mathematics problems can be solved,
proofs for the existence of natural numbers learnt since kindergarten, as well
as for the ∃∞∀∞ proof. The Definition of Existence
later verifies IINI∀I. Objects
in this paper do NOT need to be sets however, e.g. infinity is not a set, nor
is unbounded a set, yet, still, consider a non-well-funded set theory
style in reading this paper.
1. Prove that
Infinity is not Infinity (證明無限不是無限)
2. Nonexistence,
Existence, ∃∞∀∞, and ∄∅⇔∃∅ (不存在、存在、∃∞∀∞及∄∅⇔∃∅)
3. Proofs for the
Existence of the Natural Numbers (自然數存在的證明)
4.
Proofs on the Real
Numbers(有關於實數的證明). +∞>Rc, -∞<R1,
Extended R, (x,x) is smaller than [x,x]
5. Prove and Verify that Infinity is not
x (證明及查對無限即非x)
6. A Summary of the
Unbounded (「無界」的摘要)
7. Supporting Proofs for the Empty (「空無」的支援證明)
8. Off the Paper --
Resolving an Infinity Paradox, ∃∞∀∞
by an Alternative System (文外 解開無限的一個悖論,∃∞∀∞由另一系統)
9. Reflexivity of Infinity and Its
"not not not..."
10.
What is the
"Size" of Infinity?