Quick Disproof of the Riemann Hypothesis
Jonathan W. Tooker
July 6, 2019
Abstract
In this brief note, we propose a set of operations for the affinely extended real
number called infinity. Under the terms of the proposition, we show that the Riemann
zeta function has infinitely many non-trivial zeros on the complex plane.
Proposition 1.8 Suppose the additive absorptive property of ±? is taken
away when it appears as ±c?. Further suppose that ||c?|| = ? and that the
ordering is such that
n < c? ? b < c? ? a < ?
?? < ?c? + a < ?c? + b < ?n ,
for any positive a, b ? R, a < b < n, and any natural number n ? N.
Theorem 1.9 c? is
±c? = lim
x0±
1
x
.
Proof. Proof follows from the ||c?|| = ? condition given in Propositon 1.8. l
Theorem 1.10 If x = ±(c? ? b) and 0 < b < n for some n ? N, then x ? R.
Proof. By the ordering given in Proposition 1.8, we have
[?,?] = [??, x) ? [x, ?] .
It follows from Definition 1.5 that x ? R. Since c? does not have additive
absorption and the theorem states that b > 0, it follows from the ordering
that
x 6= ±c? , and x 6= ±? .
It follows from Theorem 1.6 that x ? R. l
Theorem 1.11 If a, b are positive numbers less than some natural number
n ? N, then
(c? ? a) ? (c? ? b) = b ? a .
Proof. Observe that
(c? ? a) ? (c? ? b) = limx0
1
x
? a ?
1
x
+ b
= b ? a
