This exploration of induction and philosophy of mathematics is presented as a look "under the hood" at the process of mathematical theorizing, a detailed view of how the process of induction actually works. It also provides an alternative to the mind-numbing constructs of modern logic, mathematics, and set theory, explaining the true nature of zero and empty sets and revealing the flaw in Cantor's writings on infinity.

There are original ideas here, including the author's view that zero and the empty set function as "operation blockers," as well as his explanation of why the value of the zero power of any number is always 1. The author also offers his own discovery of a new method for generating Pythagorean triples. He lays out both the deductive validation of his method and the details of his exploration of the Pythagorean equation that uncovered the relationships underlying his method.

Academics, college students, and intelligent laypersons interested in philosophy and mathematics will all find this a challenging and stimulating read. They will be rewarded with new perspectives, not only on the theoretical landscape of mathematics and logic, but also on the value in learning the mental processes involved in induction, as well as the endless opportunities for fascination and delight to be obtained from mathematical discovery.…

CREATESPACE.COM

Ah yes, the mind numbing concepts and constructs that have given rise to modern physics and related technological development and applications.

And all of the problems that cropped up in Cantor's set theory have been settled (I won't say solved). Set theory currently has no known contradictions. Please see: https://en.wikipedia.org/wiki/Set_theory

And try defining the real and complex numbers without set theory. Good luck. I am sure you will have as much luck as proving Pythagoras Theorem using only categorical syllogisms a la Aristotle.

By the way is was the Muslim mathematician al Kwarizmi or the Alexandrian Diophantis who invented algebra. Algebra reached its full flexibility during the Renaissance with the Italian mathematicians. It was Descartes and Fermat who put alebra on steroids when they combined algebra with geometry. Algebraic or analytic geometry was absolutely essential for the invention of calculus.

By the way the empty set is what makes set union, set intersection and set complementation completely general. Set theory without the empty set is like arithmetic without zero.

PS: can you name three top of the line mathematicians who are Objectivists. Pray do tell. My guess is that there are about as many first rate Objectivist mathematicians as there are first rate Objectivist theoretical physicists.

Ah yes, the mind numbing concepts and constructs that have given rise to modern physics and related technological development and applications.

And all of the problems that cropped up in Cantor's set theory have been settled (I won't say solved). Set theory currently has no known contradictions. Please see: https://en.wikipedia.org/wiki/Set_theory

And try defining the real and complex numbers without set theory. Good luck. I am sure you will have as much luck as proving Pythagoras Theorem using only categorical syllogisms a la Aristotle.

By the way is was the Muslim mathematician al Kwarizmi or the Alexandrian Diophantis who invented algebra. Algebra reached its full flexibility during the Renaissance with the Italian mathematicians. It was Descartes and Fermat who put alebra on steroids when they combined algebra with geometry. Algebraic or analytic geometry was absolutely essential for the invention of calculus.

By the way the empty set is what makes set union, set intersection and set complementation completely general. Set theory without the empty set is like arithmetic without zero.

PS: can you name three top of the line mathematicians who are Objectivists. Pray do tell. My guess is that there are about as many first rate Objectivist mathematicians as there are first rate Objectivist theoretical physicists.

I merely responded to his promo. The promo was riddled with errors. I fear for the book. I am not going to read it, by the way. Anyone who writes a math book by calling algebra and set theory mind numbing is off to a bad start.

I merely responded to his promo. The promo was riddled with errors. I fear for the book. I am not going to read it, by the way. Anyone who writes a math book by calling algebra and set theory mind numbing is off to a bad start.

That it is. But Roger will understand what I wrote.

You wrote you won't read the book.

You critiqued a promo. That's fair enough.

I can say this: the book should have a preface or introduction relating how the manuscript was vetted and by whom.

I won't read Roger's book because I can't critique it having not much in the way of mathematical bones. Because I'm careful about what I put into my brain, I never read A New Kind of Science either. I did read various promos and all I got from those was pretentiousness.

For all her intellectual greatness and life accomplishments, Ayn Rand had a lot of pretentiousness. If you admire her but don't understand this you're a Randroid or haven't yet vetted her enough.

Leonard Peikoff injecting himself into physics is pretentiousness on stilts. Rand was much more modest about science. Aristotle had his great excuse for what he was wrong about about science: he stood at the intellectual beginning of it all. Can we really blame him for the Aristotlelians? It's good shorthand but somewhat distorting.

I took Roger at his word that the book contained material along the line of his promo. In short, I -believed- his promo. This is not hearsay. This is what the author said about his very own book. Given that the book follows the line of thought indicated in the promo, I judged that the book would be a waste of my time to read. If I heard the same thing from a third party that I did not trust I would not dismiss the book out of hand. In fact I would at least skim it to find out if the book contained something which I regard as mistaken. I have corresponded with Roger before and I consider him intelligent. I think what he wrote (or claimed that he wrote) is greatly mistaken and I gave reasons in my critique of his promo (and his book). You will note that I didn't merely wrote "nonsense! chicken poop" I gave reasons for Roger to consider.

By the way is was the Muslim mathematician al Kwarizmi or the Alexandrian Diophantis who invented algebra. Algebra reached its full flexibility during the Renaissance with the Italian mathematicians. It was Descartes and Fermat who put alebra on steroids when they combined algebra with geometry. Algebraic or analytic geometry was absolutely essential for the invention of calculus.

I took Roger at his word that the book contained material along the line of his promo.

Baal has more than the promo to rely on. Here is a past thread that addressed some of the ideas in Roger's book. Included are posts by Roger, Baal, and me.

No, Archimedes did not invent calculus. Newton and Leibniz did. Archimedes anticipated some components of calculus. Or as Wikipedia says: "Archimedes anticipated modern calculus and analysis by applying concepts of infinitesimals and the method of exhaustion to derive and rigorously prove a range of geometrical theorems, including the area of a circle, the surface area and volume of a sphere, and the area under a parabola" (link).

No. Descartes and Fermat invented analytic geometry. Archimedes did not have algebra. He did his mathematics in the Euclidean axiomatic style. What he had was version 1.0 of the limit concept.

For all his brilliance, Archimedes did not have the zero.

If Eudoxus (a contemporary of Plato) had the zero, the real numbers might have been invented 2200 years before they actually were. Eudoxus liberated ratio from the ratio of units counted integrally. In fact, Eudoxus was the original "measurement omission" man, over 2 millennia before Rand was born.

Baal has more than the promo to rely on. Here is a past thread that addressed some of the ideas in Roger's book. Included are posts by Roger, Baal, and me.

Thank you for referencing the thread "The Opposite of Nothing Is/Isn't Everything" I think that thread was OL at its very, very best. It is a shame that we are so hung up on matters political at this time.

I merely responded to his promo. The promo was riddled with errors. I fear for the book. I am not going to read it, by the way. Anyone who writes a math book by calling algebra and set theory mind numbing is off to a bad start.

Couldn't agree with you more, BC. And the next time you want to condescendingly, sneeringly put down my announcements about my work, at least give a passing nod to objectivity by actually quoting me instead of putting words in my mouth I didn't say. :-P

No, Archimedes did not invent calculus. Newton and Leibniz did. Archimedes anticipated some components of calculus. Or as Wikipedia says: "Archimedes anticipated modern calculus and analysis by applying concepts of infinitesimals and the method of exhaustion to derive and rigorously prove a range of geometrical theorems, including the area of a circle, the surface area and volume of a sphere, and the area under a parabola" (link).

Archimedes used the method of exhaustion (iterated approximation) and the summation of small parts (integration). This was revealed in a heretofore "lost book" of Archimedes, The Archimedes Codex. Archimedes was a hair's breadth away from formulating the basic principles of integral calculus. If only Archimedes had the zero (sigh). We would be traveling about in Star Ships rather than jet propelled airplanes.

For those who need a little help in understanding the title of my book, it comes from one of the chapters, which is a fanciful tale of an imaginary meeting between Albert Einstein and beings from the Red Planet.

And just to be clear, "discovered" in the title is intended in the sense of "found out about" or "learned about" (not "invented" or "were the first to develop"). So, contrary to the apparent misapprehension of one over-wrought commentator here, I was not trying to rewrite the history of mathematics and deny credit to the Arabs or whomever!

Mainly, I just thought that might make a more attention-getting title than "What's the Deal with X-to-the-Zero Power?" But obviously, if the horse does not want to drink, then the horse will not drink.

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## Popular Posts

## BaalChatzaf

Thank you for referencing the thread "The Opposite of Nothing Is/Isn't Everything" I think that thread was OL at its very, very best. It is a shame that we are so hung up on matters political a

## Roger Bissell

Couldn't agree with you more, BC. And the next time you want to condescendingly, sneeringly put down my announcements about my work, at least give a passing nod to objectivity by actually quoting me i

## BaalChatzaf

Ah yes, the mind numbing concepts and constructs that have given rise to modern physics and related technological development and applications.

And all of the problems that cropped up in Cantor's set theory have been settled (I won't say solved). Set theory currently has no known contradictions. Please see: https://en.wikipedia.org/wiki/Set_theory

What is the zeroth power of zero? http://www.intmath.com/blog/mathematics/what-is-00-equal-to-1870 0^3 = 0^2 =0^1 = 0. Inductively what is 0^0? On the other hand a^b/a^-b = a^(b-b) = a^0 = a/a = 1. What is a/a when a = 0?

And try defining the real and complex numbers without set theory. Good luck. I am sure you will have as much luck as proving Pythagoras Theorem using only categorical syllogisms a la Aristotle.

By the way is was the Muslim mathematician al Kwarizmi or the Alexandrian Diophantis who invented algebra. Algebra reached its full flexibility during the Renaissance with the Italian mathematicians. It was Descartes and Fermat who put alebra on steroids when they combined algebra with geometry. Algebraic or analytic geometry was absolutely essential for the invention of calculus.

By the way the empty set is what makes set union, set intersection and set complementation completely general. Set theory without the empty set is like arithmetic without zero.

PS: can you name three top of the line mathematicians who are Objectivists. Pray do tell. My guess is that there are about as many first rate Objectivist mathematicians as there are first rate Objectivist theoretical physicists.

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## Brant Gaede

You read the book!

That was fast!

--Brant

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## BaalChatzaf

I merely responded to his promo. The promo was riddled with errors. I fear for the book. I am not going to read it, by the way. Anyone who writes a math book by calling algebra and set theory mind numbing is off to a bad start.

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## Brant Gaede

The discussion is now beyond my competence.

--Brant

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## Wolf DeVoon

Like Chris Cable often says, "I have other skills" (in your case, plenty of heroism and resolve).

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## Brant Gaede

xxx

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## BaalChatzaf

That it is. But Roger will understand what I wrote.

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## Brant Gaede

You wrote you won't read the book.

You critiqued a promo. That's fair enough.

I can say this: the book should have a preface or introduction relating how the manuscript was vetted and by whom.

I won't read Roger's book because I can't critique it having not much in the way of mathematical bones. Because I'm careful about what I put into my brain, I never read

ANew Kind of Scienceeither. I did read various promos and all I got from those was pretentiousness.For all her intellectual greatness and life accomplishments, Ayn Rand had a lot of pretentiousness. If you admire her but don't understand this you're a Randroid or haven't yet vetted her enough.

Leonard Peikoff injecting himself into physics is pretentiousness on stilts. Rand was much more modest about science. Aristotle had his great excuse for what he was wrong about about science: he stood at the intellectual beginning of it all. Can we really blame him for the Aristotlelians? It's good shorthand but somewhat distorting.

--Brant

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## BaalChatzaf

I took Roger at his word that the book contained material along the line of his promo. In short, I -believed- his promo. This is not hearsay. This is what the author said about his very own book. Given that the book follows the line of thought indicated in the promo, I judged that the book would be a waste of my time to read. If I heard the same thing from a third party that I did not trust I would not dismiss the book out of hand. In fact I would at least skim it to find out if the book contained something which I regard as mistaken. I have corresponded with Roger before and I consider him intelligent. I think what he wrote (or claimed that he wrote) is greatly mistaken and I gave reasons in my critique of his promo (and his book). You will note that I didn't merely wrote "nonsense! chicken poop" I gave reasons for Roger to consider.

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## Brant Gaede

OL is a tough place.

--Brant

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## Brant Gaede

Archimedes used analytic geometry?

--Brant

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## merjet

Baal has more than the promo to rely on. Here is a past thread that addressed some of the ideas in Roger's book. Included are posts by Roger, Baal, and me.

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## merjet

No, Archimedes did not

inventcalculus. Newton and Leibniz did. Archimedesanticipatedsome components of calculus. Or as Wikipedia says: "Archimedes anticipated modern calculus and analysis by applying concepts of infinitesimals and the method of exhaustion to derive and rigorously prove a range of geometrical theorems, including the area of a circle, the surface area and volume of a sphere, and the area under a parabola" (link).## Link to comment

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## BaalChatzaf

No. Descartes and Fermat invented analytic geometry. Archimedes did not have algebra. He did his mathematics in the Euclidean axiomatic style. What he had was version 1.0 of the limit concept.

For all his brilliance, Archimedes did not have the zero.

If Eudoxus (a contemporary of Plato) had the zero, the real numbers might have been invented 2200 years before they actually were. Eudoxus liberated ratio from the ratio of units counted integrally. In fact, Eudoxus was the original "measurement omission" man, over 2 millennia before Rand was born.

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## BaalChatzaf

Thank you for referencing the thread "The Opposite of Nothing Is/Isn't Everything" I think that thread was OL at its very, very best. It is a shame that we are so hung up on matters political at this time.

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## Wolf DeVoon

Nods in understanding. I read it, admire you for it.

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## Roger Bissell

AuthorCouldn't agree with you more, BC. And the next time you want to condescendingly, sneeringly put down my announcements about my work, at least give a passing nod to objectivity by actually quoting me instead of putting words in my mouth I didn't say. :-P

REB

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## BaalChatzaf

Archimedes used the method of exhaustion (iterated approximation) and the summation of small parts (integration). This was revealed in a heretofore "lost book" of Archimedes, The Archimedes Codex. Archimedes was a hair's breadth away from formulating the basic principles of integral calculus. If only Archimedes had the zero (sigh). We would be traveling about in Star Ships rather than jet propelled airplanes.

Please see: http://www.ams.org/notices/200808/tx080800943p.pdf

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## Brant Gaede

Thx for the great read!

--Brant

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## Peter

30, to a Roman?

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## syrakusos

Thanks, Roger. I ordered the book.

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## Roger Bissell

AuthorThanks, Michael!

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## Roger Bissell

AuthorFor those who need a little help in understanding the title of my book, it comes from one of the chapters, which is a fanciful tale of an imaginary meeting between Albert Einstein and beings from the Red Planet.

And just to be clear, "discovered" in the title is intended in the sense of "found out about" or "learned about" (not "invented" or "were the first to develop"). So, contrary to the apparent misapprehension of one over-wrought commentator here, I was not trying to rewrite the history of mathematics and deny credit to the Arabs or whomever!

Mainly, I just thought that might make a more attention-getting title than "What's the Deal with X-to-the-Zero Power?" But obviously, if the horse does not want to drink, then the horse will not drink.

REB

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## Wolf DeVoon

Explains why football, basketball, baseball, and hockey are universally shunned and ridiculed.

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