This article will quite interesting,just, because here We will know about something new.I always try to make valuable and understandable contents in just short paragraphs.
Okay,lets start,
Had you heard about additive identity of zero,
Exactly,it is very simple,the sum of any number and zero returns you same number,
Mathematically,it can be represented as:
a+0=a, where,a=any integer.
This is what we had seen about this additive identity of zero,and, this concept will be used later in this article only.
Here,I say that Why Zero is like Water, then, first you assume the Zero as Water ,and, others all numbers as colors,so, when You add any one color to the water,then,water shows that color only,
Like, If you add red color to the water,then,water-color will be red,if you mix pink color with it,then, color of water will be pink, but,We can see the color after mixing in it,we can easily verify which color is mixed with water.
Similarly,We can mathematically represented this condition as,
a+0=a;b+0;(-c)+0=(-c);and,etc.
Here,We can easily see that what's the number being added in zero, because of "Number Zero" is functions as "The Water".
But,if We add two or more colors in water,then,we can't recognize what's colors being added in the water,after sometimes.
Similarly,We can't recognize what's the numbers being added in the number zero after sometimes,
Example:-
0+3+4+5=12=0+4+2+6,
Here,We can't recognize what's the numbers being added in the "Number Zero" after sometimes.
This property we already know,but,here I explained with the physical example.
But,if we change the condition,or, simply change the algebraic expression,
Then,
You can see that earlier algebraic expression is,
a+0=a, (equation-1).
where,a=any integer (include positive and negative numbers), this is called additive identity of zero.
But,I will change something from it,
Then, somehow, mathematical algebraic expression will be,
bĂ10^m+a, (equation-2).
where,a=only positive integer,and, numbers of digit of positive-number will be,n(a)<=m,
b=positive number without zero.
n=power on "Number Ten".
Here,we can observe that in the "Equation Number-One" that "a-variable" has both values, negative and positive,
But,in the "Equation Number- Two", "a-variable" is must to be positive, because, instead of "Number Zero", we use bĂ10^n,it's means some numbers attached with zero, okay,take a example for clear the concept.
When,b=6,and,n=3,a=+34,
Then, according to the second equation,
6Ă10^3+34=6000+34=6034.
We can see easily that what's the number being added in 6000 is 34, because of Zero functions as Water.
But,if you add negative number(or, a-variable) in the 6000,then,this condition will be broken,
See,
6000+(-34)=5966,
Here,We can't easily see that what's the number being added in 6000, because,here,We used negative number,so, that's why,we can't use negative-numbers here.
By all the observations from the above,We can say that "Zero-number functions as Water".
Hmm, very cleaver way to prove the conclusion. Really impressed by your idea.
You could have taken multiplication too. But in this time , you would have to take something that gets completely dissolves in water like Salt,sugar .đđđ a 0=0 and salt water=water