To assume infinities is to concede discontinuities exist in nature as if an asymptotic curve could exist in nature and that y=1/x wouldn’t connect at x=0. The truth is far more likely that the Cartesian coordinates are better represented on a sphere rather than infinite plane. Math reflects reality to some degree less than 100%.
More on that here: phys.org/news/2013-09-mathemati … world.html
[i]Derek Abbott, Professor of Electrical and Electronics Engineering at The University of Adelaide in Australia, has written a perspective piece to be published in the Proceedings of the IEEE in which he argues that mathematical Platonism is an inaccurate view of reality. Instead, he argues for the opposing viewpoint, the non-Platonist notion that mathematics is a product of the human imagination that we tailor to describe reality.
This argument is not new. In fact, Abbott estimates (through his own experiences, in an admittedly non-scientific survey) that while 80% of mathematicians lean toward a Platonist view, engineers by and large are non-Platonist. Physicists tend to be “closeted non-Platonists,” he says, meaning they often appear Platonist in public. But when pressed in private, he says he can “often extract a non-Platonist confession.”
So if mathematicians, engineers, and physicists can all manage to perform their work despite differences in opinion on this philosophical subject, why does the true nature of mathematics in its relation to the physical world really matter?
The reason, Abbott says, is that because when you recognize that math is just a mental construct—just an approximation of reality that has its frailties and limitations and that will break down at some point because perfect mathematical forms do not exist in the physical universe—then you can see how ineffective math is.
And that is Abbott’s main point (and most controversial one): that mathematics is not exceptionally good at describing reality, and definitely not the “miracle” that some scientists have marveled at. Einstein, a mathematical non-Platonist, was one scientist who marveled at the power of mathematics. He asked, “How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality?”
In 1959, the physicist and mathematician Eugene Wigner described this problem as “the unreasonable effectiveness of mathematics.” In response, Abbott’s paper is called “The Reasonable Ineffectiveness of Mathematics.” Both viewpoints are based on the non-Platonist idea that math is a human invention. But whereas Wigner and Einstein might be considered mathematical optimists who noticed all the ways that mathematics closely describes reality, Abbott pessimistically points out that these mathematical models almost always fall short.
“I argue that there are many more cases where math is ineffective (non-compact) than when it is effective (compact). Math only has the illusion of being effective when we focus on the successful examples. But our successful examples perhaps only apply to a tiny portion of all the possible questions we could ask about the universe.”[/i]
What do you mean by “be”? How can something be if it has no boundaries?
What do you mean by “prove”? Do you mean arbitrarily define some axioms and then show how a conclusion fits?
Alright, well, my axiom is things are defined by boundaries.
Infinity has no boundary, so by my axiom, it doesn’t exist.