https://medium.com/question-time/ask-dr-silverman-8-infinity-behind-every-real-infinite-is-a-silver-lining-infinite-ca48e718070

​Early puzzles about the infinite might have begun with the ancient Greek philosopher Zeno. One version of his paradox of the infinite is this: “An arrow goes halfway to its target. It then goes another halfway, and repeats the processan infinite number of times. Therefore, it can never reach its target.” But, of course, the arrow does reach its target. Zeno lived long beforethe concept of a limit (the basis of calculus) was discovered independently by Newton and Leibniz. They showed that infinite sums can converge to a finite limit. In Zeno’s case, we can begin with one half, then add half of that (one fourth) and keep adding halves. This infinite series has the limit 1, which is the Zeno target.  
 

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https://medium.com/@scott.d.jacobsen/ask-dr-silverman-7-infinity-1-2-3-4-until-you-cant-count-anymore-171a7297f5c5 
 
There is no middle ground between the finite and the infinite, but there are some strange, non-intuitive things we can say about infinity, some of which I’ll describe. In mathematics, a set (of numbers) is said to be infinite if it can be put into a one-to-one correspondence with a proper subset (not all the numbers) of itself. For instance, the positive integers (1, 2, 3, 4, …)  form an infinite set because there is a one-to-one correspondence between them and the proper subset of positive even integers (1~2, 2~ 4, 3~6, 4~8, 5~10, etc.). A set of numbers that is not infinite is called finite. There is no one-to-one correspondence between the set of numbers {1, 3, 7, 13, and 18} and a proper subset of itself. We say that the cardinality of this set is 5 because it has 5 elements, the same as the cardinality of {10, 20, 30, 40, 50}. 

​Although the 19th-century mathematician Gauss crowned mathematics the “queen of the sciences” because mathematics is essential in the study of all scientific fields, an argument can be made that mathematics is not really a science. Science is empirical, meaning based on observations of nature, and it is potentially falsifiable by new observations of nature. In other words, new evidence can lead us to revise scientific theories, so scientific ideas can never be proved absolutely.Some mathematical ideas, on the other hand, can be absolutely proved. 
For a mathematical statement to be accepted as a theorem, its conclusion must be known to always be true whenever its hypotheses are satisfied. Mathematicians accept that a conclusion must be true based on a proof rather than empirical evidence. The Pythagorean Theorem, for example, can be proved. 
 

https://medium.com/question-time/ask-dr-silverman-5-limits-of-mind-possible-human-science-a9fc20cbe27e?
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https://www.postandcourier.com/opinion/letters_to_editor/letters-to-the-editor-we-need-to-thank-teachers-every/article_fa3f82dc-85fa-11e9-8ec1-1b524c772ae5.html

A letter writer in the May 29 Post and Courier said that separation of church and state is largely responsible for the violence in our schools and throughout society, though he provided no evidence for such an outrageous claim. He said we should act more like a Christian nation and mentioned that the Supreme Court has the Ten Commandments and the president takes the oath of office with a hand on the Bible.  To the contrary, the Supreme Court does not have the Ten Commandments. There is a representation of Moses depicted as one of several lawgivers, not as a religious figure, along with Confucius and Solon.And, it is only a custom that most presidents take the oath of office with a hand on the Bible. Several presidents, including Theodore Roosevelt, did not.

The writer also quoted Martin Luther King Jr. telling us to love our enemies, which does not make us a Christian nation. In fact, King was an advocate for the separation of church and state. He supported the Supreme Court’s decision striking down government-sponsored prayer in public schools.

Having seen the religious wars in Europe, our founders viewed religion as a private matter, without government involvement. That’s why there is no mention of God or Jesus in our Constitution. Those who wish to promote Christianity, other religions, or atheism are free to do so, but without government assistance.

HERB SILVERMAN
 

https://www.canadianatheist.com/2019/06/ask-herb-9-jacobsen/

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https://medium.com/question-time/ask-dr-silverman-4-embedment-a-tale-of-matrioshka-36568d96d918
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https://medium.com/question-time/ask-dr-silverman-3-myths-and-legends-cba315676c0c
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