A Commonsense Addition theorem

 Why will ‘only-addition’ always lead to an increase (irrespective of the initial amount)? (By ‘only-addition’, it is meant “no other activity”).

Proof : For only-addition, you need “something” before (atleast an empty space, which is some space) and that remaining unchanged – by definition.

Case 1 – initial space is occupied. 

(Note : By 'addee' it is meant "what is added to").

Here, for addition you need an addee (since initial space is occupied) and an addendum (something being added; otherwise you are not adding), and the addendum should be of the same type as that of the addee (by definition). By definition, addee remains unchanged. So upon addition, you will have the addee and an addendum – and both of the same type. Now you have 2 things of the same type, earlier you had 1 thing (only addee) of that type. 2 > 1. Hence whatever be the initial amount, adding or inflow will always lead to increase, since ‘increase’, by definition, is in a ‘numerically greater’ sense (>).

Case 2 – initial space is empty. 

Earlier there is nothing – no addee. Later there is the addendum. Something is greater than nothing. In other words, I have 1 thing – the addendum, and earlier there was nothing. Hence ....