- #1
Logical Dog
- 362
- 97
Is this proof even correct?! It places assumption on a and c NOT BEING ZERO.
Thanks in advance. I am new to proofs.
Thanks in advance. I am new to proofs.
mfb said: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 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.Bipolar Demon said:No, I think. No real number can be divided by zero
Mark44 said: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 | dWhen we say that a number a divides another b, both numbers are assumed to be integers, and a is assumed to be nonzero.
Then b = ka and d = mc, for integers k and m.
So bd = kmac
Hence ac | bd.
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.
These are the sites I frequently use to look up commands and similar:Bipolar Demon said:ok, I will learn it. :-)
fresh_42 said: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
You can do a lot with just a few tricks:Bipolar Demon said: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.Bipolar Demon said: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 workBipolar Demon said: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 adequacy of a proof can vary depending on the context and complexity of the hypothesis being tested. It is important to carefully evaluate all evidence and consider alternative explanations before determining if a proof is sufficient.
A valid proof must follow logical reasoning and be supported by reliable evidence. It should also be able to withstand criticism and scrutiny from other scientists in the field. Peer review is an important process for determining the validity of a proof.
A strong proof should have a clearly stated hypothesis, a well-designed experiment or study, reliable data, and a logical interpretation of the results. It should also consider and address potential confounding factors or limitations.
No, a proof can never be considered absolute as new evidence or information may arise in the future that could change our understanding of the hypothesis being tested. However, a well-supported proof can be considered highly reliable and accepted by the scientific community.
Reproducibility is an important aspect of scientific research as it allows other scientists to replicate the experiment or study and obtain similar results. If a proof is not reproducible, it may call into question the validity and adequacy of the original proof.