Math Is Fun Forum

Raj.01

Member

From: Pakistan

Registered: 2015-08-07

Posts: 17

Website

Found New n Interesting thing about Geometric Points

Hey all,

I searched this topic in Google but I couldn't find anything discussing this topic. This is a pure work of mine. But I don't know if its completely true, somewhat OK or completely a wrong concept.

This is why I'm sharing it here so that you expert guys will share your thoughts on this, resulting in the correction of mine (or anyone else).

<This is a part of a blog post on my personal blog, so I'm just copying the necessary part of my article>

---------------------------------------------------------------------------------------

My Personal Idea

Truly speaking, I didn’t read this anywhere so far. May be someone already discusses this aspect. But still I want to share:

Can you answer what’s zero? Let’s start counting the number of eggs you have in your refrigerator. Suppose, you’ve 3. You eat daily, an egg, then tomorrow, you’ll have 2, then on the day after tomorrow you’ll have one…At the last, you’ll have NO EGG. Now, how you’ll denote this fact mathematically?

To show that we’ve no egg, we will write it that we’ve zero eggs. Zero is basically a number that represents absence of mathematical objects.

Similarly, I feel, a point is to geometry, as Zero is to algebra, empty set is to set theory.

If I ask you, what’s 9 minus 9, what’ll be your answer? Obviously, you’ll say zero.

Similarly, while talking about set theory, if intersection of two or more sets is nothing (empty) we denote this fact by an empty set. Now, physically no empty set exists.

Then I feel, what’s the answer of this geometric problem, a line segment AB minus an equal measure of line segment DE? I’m trying to find the answer of this question, but naturally, I’m inclined to say that it must be a point! Because point has no dimensions, again, a point is to geometry, as zero is to algebra.

Now if you put several zeros on the right of some non zero number, e.g. 9, then it becomes a bigger quantity, e.g. 9,000.

But what about if you put several points together with either one another, or with some line? Obviously, several points together will form a line. Moreover, if you add more points on either to left or right side of a finite line, it’ll start extending indefinitely along left or right direction, respectively (which is one of the five postulates of Euclid).

Last edited by Raj.01 (2015-08-26 19:29:50)

---

Life is the process of narrowing down the probabilities.

NakulG

Member

Registered: 2014-09-02

Posts: 186

Re: Found New n Interesting thing about Geometric Points

This is really a interesting thought.
Zero is used to denote an absence (of anything, not a particular thing). To compare it to something i think is a fallacy. ...but i dont know how we explain this absence in a series as follows ...,-3,-2,-1,0,1,2,3,.. Vs ...3,2,1,0. Which i think is your question.
Is it that putting zeroes to the right of a number is a different zero as compared to the one represent in the above 2 series?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Found New n Interesting thing about Geometric Points

hi Raj.01

Now if you put several zeros on the right of some non zero number, e.g. 9, then it becomes a bigger quantity, e.g. 9,000.

If everyone had a good memory, you could have a counting number system in which every number had it's own symbol.  Counting might look something like this:

0,1,2,3,4,5,6,7,8,9,£,$,&,*,?,.............  Of course it isn't very practical as you quickly run short of symbols.  And if someone has made up every symbol up to a certain large value,  what happens if someone wants to add 1 to it?  Are they allowed to make up yet another symbol for the answer? And what happens if someone else has also done this but not used the same one?

Don't get me wrong.  I'm not advocating such a way of counting.  But it does help to demonstrate just how handy the decimal system is.  You only need 10 symbols and you can make any number by using 'place value'.  9000 didn't come from 9 with a few zeros added.  It's more than that.  The 9 now indicates 9 thousand instead of 9 units.  And how do I know that it's in the thousand column?  Because the zeros are showing no hundreds, no tens and no units.  Without them we don't know what place value the 9 has.  But here there are a lot of zeros that you don't need.  I've underlined the ones that are essential for place value purposes.:  000.0009000

I'm not sure how this affects your theory but I think you need to factor it in.

You might find this interesting:

https://en.wikipedia.org/wiki/Set-theor … al_numbers

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob