The question has been

answered here in detail here
With a thorough diagnostic of the interface between Real numbers and Arsistotelian infinity, the outcome
of the first Transverse Mathematics Trial’s offical publication is:
(1) Although ∞ is complying to the standard definition of a real number, we consider it at worst a non-
number or at best a loosely defined number, which we call loose number.
(2) As Potential ∞ as properties of an indefinitely large quantity of distinct numbers
(3) It lead us to the definition of strict Real numbers.
(4) With our strict Real numbers definition, we have shown that ∞ is not a strict number.
(5) Eventually we have shown that ∞ is a indefinitely large set of loose numbers.