Understanding Infinity Using Proportionality

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

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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.