As people have pointed out - and I acknowledge - maths is not my strong point. So I would be grateful to get input from those will more skill in the discipline on the following arguments:

1. $\infty=\sum_{n \to \infty} 1$
2. $= 1 + 1 + 1 + 1 + ...$
3. The first term in the series [2] is finite
4. If n is finite, then n+1 is finite
5. So by induction, the sequence [2] is finite for all natural numbers n
6. What about for n=∞? Well for no individual (n+1) step on the way to ∞, does a finite number ever become an infinite number. And infinite steps are just the sum individual steps, so it seems ∞ retains the property ‘is finite’ even at 'infinity'?

I think step [6] above is no doubt questionable, but it brings out the point: how exactly does a finite number ever become infinite? - We have no basic arithmetical operators to convert finite numbers into infinite numbers. To focus on this aspect, here is a similar argument that more graphically brings out the discontinuity between natural numbers and infinity:

A. $\infty=\sum_{n \to \infty} 1$
B. $= 1 + 1 + 1 + 1 + ...$
C. 1 is 0% of the way to counting all numbers / reaching infinity (because 1/∞=0%)
D. If n is 0% of the way to counting all numbers / reaching infinity, then so is n+1 (n+1/∞=0%)
E. (eg 100^100/∞=0% of the way to counting all numbers / reaching infinity)
F. So by induction on [C] and [D], for no natural n are we greater than 0% of the way to counting all numbers / reaching infinity
G. ∞/∞=UNDEFINED, so infinity is never in this sense 'completed'. In fact there is no number n such that n/∞=1%, n/∞=10%, n/∞=50%, so the sum of the series never gets anywhere near infinity / counting all numbers - there seems to be a massive discontinuous 'train wreck' at the end of the series associated with 'infinity' - it is unattainable?