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Mathematics

Branches:
Different Types Of Mathematics

Evolution Of Reasoning Using Compressed Representation (Mathematics?)| 18/5/17: Does excess usage of particular thoughts lead them to have compressed representation? (Clarification required, 18/5/17)

Dictionary Of Mathematics| 15/4/17: Nothing yet…

Mapping Of Two Different Lengths One To One| 15/4/17: Nothing yet; expecting notion solidity; better naming required; clarification required; (15/4/17)

Origin of Acceptance of Non Terminating and Recurring Decimals

Evolution Of Number Symbols/Sounds| 4/3/17: Nothing yet…

Identification Requirement For Solving The Problem| < 28/4/17: Nothing yet…
 
See also: A search for the Ambiguity Free Logical View on the Structure of Number Line
Some of the notions here seems to be the remembering back of notions from Euler's book Introduction to Analysis of the Infinite, or Foundations of Differential Calculus. I haven't recorded anything properly before, this has been the cause for this sloppy nature. Whenever possible, I will add the appropriate origins of notions.   

From Thales of Miletus – Wikipedia:
[Start of quote] 
He [Thales] said: Megiston topos: hapanta gar chorei (Μέγιστον τόπος· ἄπαντα γὰρ χωρεῖ.) "The greatest is space, for it holds all things".[31]
Topos is in Newtonian-style
space, since the verb, chorei, has the connotation of yielding before things, or spreading out to make room for them, which is extension. Within this extension, things have a position. Points, lines, planes and solids related by distances and angles follow from this presumption.
[End of quote]
Doesn’t that suggest on Miletus (600 B.C) to have early data on the evolution of the zero-dimensional point than Euclid (~400 B.C.)? (21/6/17)


0.9 < 0.99 < 0.999 < 0.9999 < 0.99999 < ...
0.999.... seems to indicate unsettled magnitude, does that? It seems that only settled magnitude can be located on the number, is it the case? (< 29/1/17) 
 
The space used for marking the point, seems to be producing the limit to the ability of measuring the space, i.e. we can't measure space within the mark. (19/1/17)  
 
The (ordinal) notion 1/3 as one piece of the whole when cut into three equal parts, doesn't seem to invoke any impossibility of the existence of such a piece. But, when the same fraction is expressed in decimal form (cardinal notion?) it invokes the impossibility of such a piece. This transition into of expressing ordinal fraction into somewhat decimal, is invoking a impossibility which is not felt before. But do recurring and non-terminating numbers really mean the impossibility of such a value number portion? (14/06/2016)

Are decimal results of 1/3 similar to a special case which a computer fails to execute for the right solution? (14/06/2016)

If irrational numbers [like recurring or periodic decimals] are "fractions" of the ordinal whole, then it seems they should be represented by "fractions"(?). (B5P80, 03/07/2016)

If irrationals can't be represented in a/b fractional form, and if they are the part of number line, then isn’t it that, a/b may not be said as a proper representation notation of "fractions" [via Old French from ecclesiastical Latin fractio(n-) ‘breaking (bread)’, from Latin frangere ‘to break’. --from Google]. We may need to have a different flexible/general form/notation for the fractions. (B5P80, 03/07/2016)

Where does there exist a room for non-terminating decimals as every decimal has got position in the line by rational numbers? (B5P75, 03/07/20160) 

If 0.9999...= 1, then is there any such similar possibility for other non-terminating decimals, so as to eliminate the search for the representation of  non-terminating decimals? (B5P75, 04/07/2016)

Think more on 9.000000.... and other such form being non-terminating decimals. (B5P75, 04/07/2016)    

I should read more on Babylonian cultural development of fractions. (B6P28, 07/07/2016, Exploratory)

What about creating a number system with base as one, with number zero? It might provide a way of looking at similarity between numbers like, say, 9.0000..., 9.3333... and $\pi$. (B5P25, 07/07/2016, Intuition) 

Egyptians seems to have had no conception of fraction with denominator and numerator, i.e as the one which needs to be further solved. They might have thought them to be in the simplified form itself, with their origin either from half of a farm field or any other such, as like every other natural numbers which had their origin likewise in greater number of lotus, marks on tally, cattle hobble, etc. (08/06/2016)

Think more on the addition mechanism behind $\sqrt{2}*\sqrt{2} = 4$. (<31/07/2016)

Experience (E)| From Midhat Gazale's Number: From Ahmes to Cantor (Page 59): "The decimal system has been established, somewhat foolishly to be sure, according to man's customs, not from natural necessity as most people would think. --Pascal."
Try searching on the books read, or experience had by Pascal before coming to this above conclusion. (23/1/17)
From Susan Carey's The Origin of Concepts (Page 3): "Different types of processes, operating over three different time courses (individual learning, historical/cultural construction, and evolution), underlie the formation of our conceptual repertoire. Some concepts, such as object and number, arise in some form over evolutionary time. Other concepts, such as kayak, fraction, and gene, spring from human cultures, and the construction process must be understood in terms of both human individuals' learning mechanisms and sociocultural processes. Humans create complex artifacts, as well as religion, political, and scientific institutions, that themselves become part of the process by which further representational resources are created."
 

Abstraction Before Paintings? | 26/12/16: E: The following is extract is taken from Genevieve von Petzinger's The First Signs: Unlocking the mystery of the world's oldest symbols. 
At the moment, we have no sites with portable art or other symbolic artifacts to provide us with clues as to how our ancestors progressed from those first manifestations of abstract expression in Africa to the skillful imagery on cave walls in Europe and beyond. 
Thought (T) : Did abstract nature come before details (like paintings) ? (26/12/17) 
Are details the product from the exploration of faint general notions? (5/1/17) 
Then would we be aware of math structures before details? (clarification required, 7/2/17) 
If math comes before in evolution stages, would it be easy to acquire first than details? Why? Do you think early stages are more easy to acquire than the later developed ones? (7/2/17) 
Doesn't the paintings require small curves, lines, etc.? This is not to say on abstract meaningful signs to have come first, but to suggest the ability of making at least the marks, which can be called abstract symbols if they embed meaning in them or just as the marks without meaning. (17/1/17) 

Reality of Complex Numbers: Think on discovering a spatial representation of complex numbers, which reduces to usual Cartesian coordinate space when imaginary part becomes zero. (13/07/2016)

Complex Numbers: Complex numbers seems to be generated from the wrong arrangement of math elements. (B5P76, 03/07/2016)

Spatial positional number system: Incredible, but may seem no surprise now, the use of position of elements itself to have a meaning. What other properties can you use to ease the number use even further? We can try exploiting different spatial positions other than just the horizontal ones, to have different meanings. (B5P25, 07/07/2016, Intuition/Exploratory)

Reasoning in Math | 15/08/2016: Experience (E)| I solved an equation, which gave certain value for the expression, even though the result was true from which it was derived, I was looking for another way of looking at the expression which satisfied me on it to be the case. (B[ook]6P[age]32, 15/08/2016)Thought (T)| Was I looking for an understanding derived from other-than math: the practical case? (B6P32, 15/08/2016)

Ease Door of Math| 01/11/16: Unlocking the understanding of infinitesimals/irrational numbers, seems to unlock the ease door of math. (B11P80, 01/11/16)
 
Does the set X = {1,2,3} has nothing (let us give it any sign, say n) as an element in it?

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