Oresme-TEST to see if a Math professor is worthy or a fool of math

Oresme-TEST to see if a Math professor is worthy or a fool of math #76.4 Math-Professor-text 8th ed.: TRUE CALCULUS

Now let me talk about a situation that somewhat happened to me, in order for the reader to understand the Test involved here.

Suppose I or you are a physicist going into a classroom of mathematicians and taught by a math professor and we know what today's lecture topic is going to be about-- introduction to Series and in particular the so called proof that the Harmonic series is divergent.

Now in this post we are going to also learn why mathematicians are often the butt-of-the-joke in jokes of "there is a engineer, physicist and mathematician to screw in a light bulb..."

Anyway we attend the class on the topic of Oresme and sit ourselves down in a desk surrounded by math students and the math professor.

Now the Math Professor talks about the Counting Numbers, 0, 1, 2, 3, 4, . . . only he calls them the Naturals, and then talks about a Sequence such as those counting numbers 0, 1, 2, 3, 4, . . . *and about other sequences such as 1, 1/2, 1/3, 1/4, 1/5, . . .

Then the professor introduces the concept of Series and explains it is a sequence that has an operator between the terms of the sequence.

And he talks about the Harmonic Series of 1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 . . . and says it goes out to infinity.

Alright so far and we, us two physicists have our minds active, alert and going ahead of the professor where our minds say this:

"So the Naturals are the smallest set of whole numbers and they go to infinity, only the professor never defined what he means by infinity by giving us a border between finite and infinite, yet we do know that 0 is the smallest Natural and 1 is the second smallest, so a Series of 0 + 0 + ... out to the professor's nebulous infinity would be a sum total of 0, while the series 1+1+1+.... out to his nebulous infinity would be a sum of the smallest infinity for the Naturals since 1 is the second smallest number of the Naturals. The series of 0 cannot be the smallest infinity because its total is 0 which is a finite number. Now the professor brought up the topic of the Harmonic Series 1 + 1/2 + 1/3 + 1/4 + 1/5 +.... and it added up at infinity which is nebulous because the professor never gave the border between finite and infinite, that the Harmonic Series cannot possibly be divergent since the smallest divergent series is the 1 + 1 + 1 + 1 + ..... series"

So that was the forward progression of the thoughts in the minds of the two physicists sitting in the classroom of mathematicians. For the physicists have logic while the mathematicians seem to be running on something less than logic.

Because the math professor now argues a alleged proof that the Harmonic Series is divergent and is equal to infinity. The professor says that in the century of the 1300's Oresme grouped the terms of the Harmonic Series where he saw that 1/3 + 1/4 is larger than the previous term of 1/2, and where (1/5 + 1/6 + 1/7 + 1/8) are larger than 1/2. And came to the conclusion that with such a grouping that the series must diverge and go to and equal infinity.

"So, where is the mistake? Where is the loophole of logic?"

Now, to the two physicists in the classroom, us two are rather taken aback by this news. For, what we see is that the professor never defined a border of finite to infinite, and yet the concept of infinite is used liberally throughout the alleged-proof, not only in the grouping but in the actual count of the terms of a series.

The length of the series 0 + 1 + 2 is a length of 3 terms. The length of the series 1+ 1 + 1 + 1 is a length of 4 terms.

Now, if you never define infinity with a borderline, how is it that you or Oresme can increase or decrease the length at will, at wishy washy will?

In the 10 Grid where we pretend 10 is the border of infinity and where 10 is the last and final finite number, in such a Well Defined infinity and series definition of terms, we have the series 1+1+1+1+1+1+1+1+1+1+1
going to infinity because it has eleven terms of 1 and its sum is 11 which means it is divergent and is equal to infinity since 11 is an infinite number in the 10 Grid.

In the 10 Grid we also have a Harmonic type of series in 1 + .1 + .2 + .3 + .4 + .5 + .6 + .7 + .8 +.9 + 1.0 which has 11 terms since 11 is the smallest infinity counting number. And the sum total of that Harmonic type series is far smaller than 11 and such is a convergent and finite series.

So, to the Math Professor and all the math students in the classroom, they are not bothered by the fact that they fail to define these items:

(1) to use finite versus infinity you must state a border between them so that you cannot wishy washy have more terms in one series than in another series

(2) when you state the border, the border is what tells you whether the series diverges or converges

(3) if you do not state a border, you cannot use the concept "goes to infinity" because you have no connection with finite.

So, now for the Joke, we have three persons, one a engineer, one a physicist and one a mathematician. And the question given to the three, is "What is the smallest series that goes to infinity and is thus, divergent?" The engineer who is practical says that well, a Series is a sequence of terms and the number of terms needed to be at infinity is the infinity borderline, so the smallest infinite Series is 1 + 1 + 1 + 1 +....
Next comes the physicist and he is a bit more refined with an added touch to the problem, for he says the same thing as the engineer but adds on a nice touch with 1_1 + 1_2 + 1_3 + 1_4 + . . + 1_infinity border +1. You see the physicist numbered his terms so that there are exactly infinity border terms of adding 1 with one more additional so that the series is 1 more past the largest finite counting number."

Now comes the mathematician's turn to answer, and his answer is the same as the math professor and students of math, that you never define what it means to be infinite yet you freely and profusely use a nebulous concept that has border, has no relationship to finite. And you end up with the fakery that fractional Series diverges and equals infinity in sum total.

People of commonsense, of practical knowledge, of a tidbit of logic in their minds realize that the smallest Series in math that goes to infinity has to be the Series 1 + 1 + 1 + 1 + ...+1. Otherwise, if you have fractional series like the Harmonic going to infinity and diverging means that you have a boatload of definitions that are phony fake nebulous definitions.

So, here is the test on whether you have the modicum of logic to be a mathematician or a math professor, is whether your mind accepts and believes such trash as the harmonic series is divergent or whether you see that with a well defined infinity, that the smallest divergent series is 1 + 1 + 1 + .....

I am afraid that almost all the math professors of today are failures of mathematics and lack that shred of logic to be a mathematician. And worse yet, they teach this propaganda brainwash to students who must accept their phony argument in order to get a good grade.

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Drexel's Math Forum has done an excellent search engine for author posts as seen he
http://mathforum.org/kb/profile.jspa?userID=499986

Now, the only decent search for AP posts on Google Newsgroups, is a search for for it brings up posts that are mostly authored by me and it brings up only about 250 posts. Whereas Drexel brings up nearly 8,000 AP posts. Old Google under Advanced Search
for author, could bring up 20,000 of my authored posts but Google is deteriorating in quality of its searches, likely because AP likes an author search and Google does not want to appear as satisfying to anything that AP likes. If AP likes something, Google is quick to change or alter it.

So the only search engine today doing author searches is Drexel. Spacebanter is starting to do author archive lists. But Google is going in the opposite direction of making author archived posts almost impossible to retrieve.

All the other types of Google searches of AP are just top heavy in hate-spam posts due to search-engine-bombing practices by thousands of hatemongers who have nothing constructive to do in their lives but attack other people.

Now one person claims that Google's deteriorating quality in searches of science newsgroups is all due to "indexing". Well, that is a silly excuse in my opinion, because there is no indexing involved when one simply asks for a author search. No indexing involved if one wants only the pure raw complete list of all posts by a single author. And Google is called the best search engine of our times, yet I have to go to Drexel to see 8,000 of my posts of which I had posted 22,000 to 36,000 posts from 1993 to 2013. It is a shame that Drexel can display 8,000 while Google has a difficult time of displaying 250 of my authored posts. Where the premiere search engine of Google is outclassed by Drexel and even by Spacebanter.

Archimedes Plutonium