we moved to wordpress!

this blog is closing down, the new link for my blog is:

dominvsmevs.wordpress.com

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Understanding Infinity Using Proportionality

in a precious article, we used black holes to understand infinity; this time, we'll use proportionality.

image source: google.com

a ∝ b

a = k(b);

removing the proportionality and adding the constant.

k = a / b

now, the above equation can be converted into two proportionality each keeping 'a' or 'b' constant respectively.

 k ∝ 1 / b 

keeping 'a' constant;

or

k ∝ a / 1

keeping 'b' constant;

let's take the equation with 'a' constant:

 k ∝ 1 / b 

as 'b' will approach '0', k will approach 'infinity';
b --> 0 , k --> ∞ ;

when b will become zero, k should become infinity;

∞ ∝ 1 / 0
or
∞ = 1 / 0 * a
or
∞ = a / 0

where 'a'  is any positive number.

let's take the equation with 'b' constant:

k ∝ a / 1

or

k ∝ a
as 'a' will approach 'infinity', 'b' will also approach 'infinity';
a --> ∞ , k --> ∞ ;

when 'a' will become 'infinity' , 'k' should also become 'infinity';

∞ ∝ ∞
or
∞ = (b)∞

where 'b'  is any positive number.

∞ = (b)∞ implies that multiplying any positive number with infinity will only result in infinity.

∞ = a / 0 implies that dividing any positive number by zero will only result in infinity.


comment below if you have any questions or simply to start a discussion.

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Zeno's Paradox

let's say, you are standing at a point 'a' and want to move towards point 'b'; what if i told you that mathematically, you can't reach point 'b'.

image source : commons.wikimedia.com

this is the famous 'zeno's paradox', and it has been around for quite some time.
to get from 'a' to 'b', first you'll have to travel half the total distance; then the half of the remaining distance or a quarter of the total; then half of the remaining distance and so on. physically, you would reach your destination but mathematically, it should add infinite number of times; surely it would converge to the total distance but will never be exactly equal to it.
now, the solution of the paradox was found with the discovery of 'plank's length' which is the smallest separation between two objects (1.6 x 10^-35 m). once the distance between the person and the destination is close to plank's length, it would reach it's destination because travelling half the distance then would reduce the separation to less than the plank's distance which is physically impossible.
there are some other variations of this paradox too but the solution is same for all.

image source : google.com

in the above instance, as the person approaches the turtle, the turtle also move a little bit. 

let's say the man is at point 'a' and the turtle is at point 'b'.as the man reaches 'b' from 'a', the turtle moves to 'c'.as the man reaches 'c', the turtle moves to 'd' and so on.

when the distance between the person and the turtle is equal to plank's length he would overtake the turtle.

this was a fun little paradox and for it's considerable history, the solution was not known.

comment below to start any discussion or ask anything about it.

published by zain ul abideen.

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The Eventual Fate Of Our Universe

everybody you know, you love, is going to die.everything that you own or you will ever own is going to be rendered useless; and in the grand scheme of things, the universe itself, is going to die.no one can escape death; you are going to watch your loved ones die (assuming you lived long enough) and in the end, they (the ones still alive) are going to watch you die.death is eventual and every soul will get a taste of it, tomorrow if not today.

image source : google.com

if the universe continues to accelerate in it's expansion ,given infinite time, every point in the universe will become infinitely distant from any other point and no light from a point will reach any other point; and the last of the creations will die a lonely and dark death.

"watch the end through dying eyes,

now the dark is taking over."

~ breaking benjamin

if the universe, for some reason, stops in the acceleration of it's expansion, the might of gravity will take over and the universe will start to fall in itself.the stars would go supernova and form back-holes which will then, in time, consume the whole mass of the universe.through hawking radiation, these black-holes would then evaporate, a little by little, and after an infinite amount of time, the universe will fade into nothingness.it will be at this point that the universe will become a true void; will reach it's state of maximum entropy and a temperature of absolute zero.

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