I think you gave the perfect reasoning for this. As I have stated before about the Stanford mathematician, he was actually teaching real analysis, where we don't have prior knowledge of these numbers. Thanks.
Hi
Since I am not a real expert and I am just starting to self-teach maths in my part-time, I asked another expert and his answer was:
The problem with using √2 in your definition of the set is due to the fact that you are working in the rationals, defining a set of rational numbers and...
I have a video of Stanford mathematician Keith Devlin talking about this particular aspect of why you can't define in terms of real numbers for proving something about rational numbers.
He in particular worked out this proof without going anywhere near real numbers.
sqrt(2) is not in any...
I think it is a big mistake to say that x less than sqrt(2), earlier you said x belongs to rationals, but sqrt(2) is not rational, it is real. You cannot just take some thing from real number system for defining something in rationals.
Yes, your'e right. sqrt of 2 belongs to real numbers and that is the exact reason, why we cannot use it for defining incompleteness of rational numbers. You can use, as Steve said "set of rationals whose square is less than 2". Because 2 belongs to rationals, but sqrt 2 doesn't.
It is this...
Actually Steve didn't say that, he said "square less than 2", which is completely different from square root of 2, because the set of rationals doesn't contain square root of 2 and therefore you cannot use that to test completeness. But of course the equivalent square less than 2. Which doesn't...
Thank you for your inputs/opinions.
I think I should explain more about myself. I am an Indian citizen and I am currently residing in Czech republic, where recently I discontinued my PhD in Immunology. Since childhood I was always interested in becoming a scientist and all the famous...
I graduated from Medical school. Then wanted to pursue my career in research. I chose Immunology and I was doing PhD. But my skills were not good and I was fired during my studies. My supervisor said that I am smart and clever but I don't have skills.
I always wanted to be a scientist and I...
I believe what you suggested is more appropriate for this context.
Thanks a lot.
At first, I thought I would just write the question and get the answer. But you made me think. I appreciate your policy. Thanks again.
I am sure I will have a lot more questions to ask. :)
I think I know the definition for those.
Do you think I have to make 7 ml(acetic acid) + 40 ml(methanol) and add water up to 100 ml?
Or Do I have to make 7% acetic acid (7ml in 100ml of water) and then add it to 40% methanol? If I do the 2nd way, how much of acetic acid I need to add to...
I am totally confused, I don't understand how to solve it. :(
Please see also: http://www.sigmaaldrich.com/etc/medialib/docs/Sigma/Datasheet/b2025dat.Par.0001.File.tmp/b2025dat.pdf
I need to make this solution. Also I need to make 10% acetic acid in 25% (v/v) methanol.