Physics contradicts maths - how is this possible?

The answer is quite simple.If x is time and y is distance to the wall then the flies motion is described as:y = 1 - xy = 0 when x = 1. So the fly lands on the wall at one second. All you're doing is taking values that are not 1 and then pointing out that the fly isn't on the wall for any of them. Of course it isn't, because the values aren't 1.Limits would be used if you wanted to show that y(x) is continuous at x = 1. i.e., lim x->1 y(x) = y(1).Zeno's Paradox would more relate to the fact that since we know the fly lands on the wall at 1 second using the standard selection process of just picking 1, your limiting selection process should have 0.9 + 0.09 + 0.009 + ....... = 1.
Basically 0.9 + 0.09 + 0.009 + ....... should equal 1, but does it? It was a question the greeks couldn't answer and a full understanding of the continuum had to wait a long time. However that maths says the fly landing on the wall regardless of this question.

Here's another cool fact. At least I find fascinating.Take the real numbers. Obviously within this set of real numbers are the set of integers (whole numbers). Now another set within in the real numbers is the set of rationals (fractions). The set of rationals contains the integers since any whole number like 3 is also a fraction when written as 3/1.Now the next set we have is the algebraics. The algebraics are any number which is the solution to a "high-school algebra" equation like: X^3 + X^2 + 3X = 4. Basically anything that is a root of a polynomial, for people who know what that is. This set includes numbers like the square root of 2(solution of x^2 = 2) which aren't fractions. However it also includes fractions. So it's an even larger set of numbers than the rationals. However it doesn't include things like Pi.Now an even bigger set is the computables. These are any numbers for which there exists (even in theory) an algorithm which can compute their digits one by one. This includes all of the algebraics, but it also includes numbers like Pi and e, since we can compute their digits one by one.Basically the computables contain every single numbers you've ever heard of and all numbers that can theoretically be found with a computer if you had infinite time to find them.Now what about the Real numbers that are left over, the so called uncomputables. It turns out they're most of the real numbers.
This means for instance that between 3 and 4, every fraction, every algebraic and every computable number forms just a vanishing amount of the numbers between 3 and 4.Most of the numbers between 3 and 4 are numbers which can never be found or described, even in theory given an infinite amount of time.

(Yeah, a (very) rough sketch of the proof is that any given algorithm is specified by a certain number of symbols which can be "Gdel Numbered". That is you can assign a natural number to any given algorithm. Since the cardinality of the Natural numbers is Aleph-Zero, then the cardinality of the computables is also Aleph-Zero. As you know the cardinality of the Reals is greater than Aleph-Zero, hence most reals are uncomputable.)This is a major bone of contention with constructionists. As you know a continuum like the Real numbers is needed to do analysis and calculus. This is because of properties like convergence e.t.c. that Modulous and sinequanon have been talking about. However if most of the Reals are numbers that can never be described, labelled, reached, e.t.c. (even in principle) then you get this picture of the Real numbers as being like the night sky. All the numbers we use are just pin point stars in the vast black of uncomputables.
However even though we never use all that black, never even speak of it, you need it (formally) for calculus.Certain people are uncomfortable with most of the Reals being simply "formal junk" that's only generated to do calculus. This caused a program at the start of the twentieth century which attempted to see how much of the reals you can remove and still have calculus work. It turns out that removing the uncomputables means the fundamental theorem of calculus no longer holds.

Yep, sure there are now people even more extreme, the ultra-finitists. They don't even agree that big numbers (e.g., 10^google) are sensical.To be fair though the people who don't like the uncomputables are constructionists-lite. They don't share the views of other constructionists, they're just a bit unsettled by analysis being based on numbers you can't talk about. I love the axiom of choice. It implies stuff that is totally crazy and you intuitively feel like rejecting and yet if you get rid of it you lose stuff that is totally obvious and necessary from every area of maths.