# I Is this proof adequate?

1. Jan 14, 2017

### Logical Dog

Is this proof even correct?! It places assumption on a and c NOT BEING ZERO.
Thanks in advance. I am new to proofs.

2. Jan 14, 2017

### Staff: Mentor

If a|b, can a be zero?
If c|d, can c be zero?

If not, that case is not relevant for the proposition.

3. Jan 14, 2017

### Logical Dog

No, I think. Nonumber can be divided by zero. Edot: I was confused because it said all are in integers

Any other (creative) way to do this proof? (using a direct proof method)

Last edited: Jan 14, 2017
4. Jan 14, 2017

### Staff: Mentor

No number can be divided by zero. Zero doesn't belong to multiplicative groups by definition of the group properties and zero as the additive neutral element.

The other way around, if multiplication (of all elements including zero) doesn't form a group, one can have $a\cdot b =0$ $a$ and $b$ are then called zero divisors. E.g. the remainders of divisions by a non-prime have zero divisors, $2\cdot 3 \equiv 0 \mod (6)$.

5. Jan 14, 2017

### FactChecker

It looks good to me. Maybe it could use a little word-smithing.

6. Jan 14, 2017

### Staff: Mentor

The order of your proof needs work. You say
"Thus $\frac{bd}{ac} = l, l \in \mathbb{Z}$"
Then you talk some more about $\frac{bd}{ac}$, which should come before saying, "Thus..."
Here's what I think is a more direct proof:
a | b and c | d
Then b = ka and d = mc, for integers k and m.
So bd = kmac
Hence ac | bd.​
When we say that a number a divides another b, both numbers are assumed to be integers, and a is assumed to be nonzero.
Edit: Fixed some typos caused by switching letters.
In the future, please post your work here directly, rather than as an image. Everything you did can be done using TeX. If you are uncertain how to use this, take a look at our tutorial, under INFO --> Help/How-tos. The LaTeX tutorial is listed there.

Last edited: Jan 14, 2017
7. Jan 14, 2017

### Logical Dog

ok, I will learn it. :-)

Last edited by a moderator: Jan 14, 2017
8. Jan 14, 2017

### Staff: Mentor

9. Jan 14, 2017

### Logical Dog

10. Jan 14, 2017

### Staff: Mentor

You can do a lot with just a few tricks:
Fractions: $\frac{ab}{cd}$
Script: $\frac{ab}{cd}$

Exponents, subscripts: $c_1x^2$
Script: $c_1x^2$

Integrals: $\int_a^b f(t) dt$
Script: $\int_a^b f(t) dt$

These are probably the ones I use the most

Matrices: $\begin{bmatrix} 2 & 3 \\ 0 & 1 \end{bmatrix}$
Script: $\begin{bmatrix} 2 & 3 \\ 0 & 1 \end{bmatrix}$

11. Jan 14, 2017

### Staff: Mentor

The best thing is $\text {$ math $}$ is fast to type.
I even downloaded me a tiny program (AutoHotkey) that allows me to add shortcuts to my keyboard. E.g. I have Alt+f which makes me \frac{}{} for quotients. One just have to ensure not to overload the shortcuts one usually uses, like Ctrl+c. But even then, this little helper can easily be switched on and off.

12. Jan 15, 2017

### MAGNIBORO

the best way to learn this is That the internet make all the work
https://www.codecogs.com/latex/eqneditor.php