Rejecting the Infinite qua Infinite Is Erasing the Great 19th Century Progress in Mathematics

‘What Is Mathematics?’ is a popular book written by the German mathematician, Richard Courant (with Herbert Robbins). In 1934, he brought the great 19th century progress in mathematics to th USA and worked in the New York University. On page 77 of this book, one learns that Courant also brought with him (1) the infinite qua infinite, which is a noun or determinate infinite, and (2) the infinite (without end) or indeterminate, which is an adjective. Since Courant was born in 1888 and thus after Georg Cantor found the transfinite numbers, it seems likely that he also brought Cantor’s genuine infinite (the infinite qua infinite) and non-genuine infinite (the infinite without end). One wonders why our mathematicians and scientists are not considering both infinities. Without both infinities, it seems that a half-world exists rather than a whole world.

If one investigates Courant’s book further, one learns that the complex numbers, like the negative numbers, were created in order to extend the number domain so that unsolvable equations could be solved. The extended domain of complex numbers was developed and was based on definitions, which are freely made. But, this development maintained the rules and properties of the lower domain. Cantor developed the transfinite numbers the same way.

Interestingly, such progressive extensions are usually opposed, by the same field of thought, the Aristotlean logicians. Cantor was attacked by the logicians of his time. He spent much time in hospitals due to the stress. Today, such logicians continue to oppose such progress by attacking my character and my scientific proof of God without ever reviewing it. This character assassination has continued by atheists ever since the book appeared on the market in June 2006. As an engineer, I know the importance of progress for the USA. But, I also know that this progress will be denied with atheism. Atheists do not know that progress of a nation is possible only when man's work is consistent with God's work.

Like extending the number systems, I used my personal freedom to extend the finite world into the infinite world of God. This extension shows that God originates all finite things. This extension is essentially my proof of God. Essentially, I connect the ‘infinite qua infinite’ to the ‘infinite without end.’ Thus, my extension is not much different from extending the real number systems to the complex numbers and transfinite numbers.

Since mathematicians cannot extend the number domain beyond the transfinite numbers and into some higher world of numbers, it seems time for them to accept the infinite qua infinite and start developing Cantor’s transfinite numbers. By developing the transfinite numbers, I expect science to uncover many hidden secrets such as new energy sources.