Thoughts on Mathematics

Although I am not a mathematician, I do have certain common sense ideas (at least to me) that seem certain to me about mathematics. I will provide my thoughts here and if any mathematicians who read them should find them comical, then go ahead and have a laugh; I am happy to entertain you.

To begin with, from what I have read about the axioms of Peano and Frege, they consider zero and infinity to be numbers. But I cannot see how either zero or infinity can be numbers. Number has to be a limitation of something but zero does not limit anything. Zero actually means "no number" and how can this be a number? Zero actually means nothing. Nothing never figures in mathematical calculations. Nothing can be the result of a mathematical calculation such as 1-1=0, but cannot figure in the calculation itself. One cannot subtract, add, multiply or divide by using zero. Zero cannot be a number. The calculation 1+0=1 cannot be a true calculation since it merely affirms that nothing can be added to one.
Infinity also cannot be a number because it too does not limit anything. One cannot add, subtract, multiply or divide using infinity. Infinity cannot figure in any calculation, although it too can be the result of a calculation. There can be no such things as infinite numbers or classes of infinite things because all such things are limited by definition. The formula "n equals n+1" cannot describe infinity because if "n" is a number then it has to be finite no matter how large, and if one adds a one to it then one only has a larger number by a factor of one. This formula merely confirms that numbers must be finite. If "n" is considerd to be infinity itself, then it cannot equal itself because this would be a limitation, and also a one cannot be added to it. Infinity can only be absolutely unlimited. This can be the only true definition of infinity since any other definition would, of necessity, be limited.
There are some strange similarities between the ideas of zero and infinity. Neither of these ideas can be understood by the finite mind, and yet somehow we have the ideas of them and can use them in limited ways.
Some empirical philosophers speculate that the idea of infinity has been acquired by the idea of one end following another end somehow leaping to the idea of infinity. But the idea of one end following another end must always be a finite idea since this series always comes to an end no matter how far it goes. The leap to infinity that the empiricists imagine can only be a metaphysical and speculative leap which they do not believe ever reveals any truth.
The finite mind also never experiences nothing except as an idea. We never see nothing. We only see things through nothing. Nothingness can never be seen or felt. We cannot imagine nothing. We can imagine a dark or light screen but not nothing. Nothingness is always an inference of the mind. Space cannot be nothing in a direct way. Space is an extension between objects, but the idea that space is nothing is merely an inference.

All of this raises the question: How did we ever acquire the ideas of nothing and infinity? These ideas must be real because unreality always lies beyond experience in the realm of nothingness or the unknown. These ideas also must be real because we can use them in limited ways. Unreality is always useless. The only possible answer to this question must be that there exists an Infinite Mind who gave these ideas to the finite mind.