I How can I improve my proof skills with internet resources?

[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.

 

[mfb]

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

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

 

[Logical Dog]

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

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

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)

 

[fresh_42]

No, I think. No real number can be divided by zero

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, $2\cdot 3 \equiv 0 \mod (6)$.

 

[FactChecker]

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

 

[Mark44]

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.

 

[Logical Dog]

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.

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.

ok, I will learn it. :-)

 

[fresh_42]

ok, I will learn it. :-)

These are the sites I frequently use to look up commands and similar:

https://www.physicsforums.com/help/latexhelp/
http://detexify.kirelabs.org/symbols.html
https://www.sharelatex.com/learn/Spacing_in_math_mode

It's easy. I mean even me got it

 

[Logical Dog]

These are the sites I frequently use to look up commands and similar:

https://www.physicsforums.com/help/latexhelp/
http://detexify.kirelabs.org/symbols.html
https://www.sharelatex.com/learn/Spacing_in_math_mode

It's easy. I mean even me got it

thanks a lot...I am just scared of having to program anything (last time I programmed things didn't go too well). I will ytry it :-)

 

[Mark44]

thanks a lot...I am just scared of having to program anything (last time I programmed things didn't go too well). I will ytry it :-)

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

 

[fresh_42]

thanks a lot...I am just scared of having to program anything (last time I programmed things didn't go too well). I will ytry it :-)

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.

 

[MAGNIBORO]

thanks a lot...I am just scared of having to program anything (last time I programmed things didn't go too well). I will ytry it :-)

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