A very basic tutorial.
How to deduce that $0 \times 2 = 0 $?
1) The translation for $a \times b$ when $b \in \mathbb{N} $ is $a + a + a \cdots (\text{b times})$
Therefore, $0 \times 2 = 0 + 0$. Going a little elementary — No apples and no apples are no apples.

2) Zero is considered as the additive identity in Mathematics. The property says:
$x + 0 = x$
Assume that $x = 0$, so $0 + 0 = 0$

Question

A very basic tutorial. 
How to deduce that $0 \times 2  = 0 $?
1) The translation for $a \times b$ when $b \in \mathbb{N} $ is $a + a + a \cdots (\text{b times})$
Therefore, $0 \times 2 = 0 + 0$. Going a little elementary — No apples and no apples are no apples.

2) Zero is considered as the additive identity in Mathematics. The property says:
$x + 0 = x$
Assume that $x = 0$, so $0 + 0 = 0$

parthkohli · Answer

Source: I posted this in M.Se

parthkohli · Answer

Refresh the page, I edited the thing.

anonymous · Answer

It's via definition.

parthkohli · Answer

This might not be good for M.Se, but it's cool for OS :P

unklerhaukus · Answer

should this arrow really go both ways?$$x + 0 = x\Longleftrightarrow x \in \mathbb{R}^{+}$$

parthkohli · Answer

Yeah.

anonymous · Answer

No.

anonymous · Answer

Consider $e+ei.$

parthkohli · Answer

Let me edit my tutorial then :O what is the correct notation btw?

unklerhaukus · Answer

the additive identity only holds for positive real numbers?

parthkohli · Answer

R+ are the extended real numbers, right?

anonymous · Answer

$x+0=x$ holds for all numbers $x.$ (Exclude set theoretic-numbers; I am uncertain about them.)

parthkohli · Answer

How do you denote all numbers?

anonymous · Answer

You don't. As far as I know. I think $\mathbb{C}\cup \mathcal{T}$ would be the best way?

parthkohli · Answer

Oh, well. We could just write $x + 0 = x$. And as I said, this is a basic tutorial.

anonymous · Answer

$\mathcal{T}$ for transcendentals.

unklerhaukus · Answer

$$x + 0 = x\Longleftarrow x \in \mathbb C$$
$$\mathbb R \subset\mathbb C$$

parthkohli · Answer

My tutorial didn't go as well. I closed it.

unklerhaukus · Answer

just put $$\Longleftarrow$$
instead of
$$\Longleftrightarrow$$

anonymous · Answer

Rhaukus, you think that transcendentals aren't the same under the additive identity...?

parthkohli · Answer

I blame @Limitless for telling me that "if and only if" is "\iff or \Longleftrightarrow" :P

unklerhaukus · Answer

i dont think iff is right

anonymous · Answer

I mean, it's true that $x \in \mathbb{C} \Rightarrow x+0=x$, but it's a tad misleading.

anonymous · Answer

I would think that the most general statement would be $x \in \mathbb{C}\cup \mathcal{T} \Rightarrow x+0=x.$

parthkohli · Answer

Well. Leave it. This tutorial is closed. ;)

unklerhaukus · Answer

i dont know anything about the  transcendentals

anonymous · Answer

@ParthKohli, no offense intended, but I'm genuinely interested in what Rhaukus's thoughts are.

parthkohli · Answer

Yeah. That is why I thought that this tutorial failed :)

unklerhaukus · Answer

this tutorial was a learning experience