Ok, I suppose you are only asking about real functions of one variable,like f:R->R. You only have to think of how symmetry is "translated" in algebra.
If a function has a x-axis summetry, then it simply is not a function, with the classic definition, or it's a multivalued function, because the...
As pardesi mentioned, you can't say that two functions have the same limit, if this limit doesn't exist. Anyway, the thing that causes you problems is the limit of sin(1/x) when x->0.
As pardesi also mentioned, this limit doesn't exist. There's a theroem that says that a limit of a function...
I will just add that if you look at the definition of the limit (-> http://mathworld.wolfram.com/Limit.html ) it says "for any ε>0 there exists δ ... with 0<|x-x1|<δ" and not just |x-x1|<δ. So we don't care about the case x=x1. This actually shows the "fake" and "real" zero concept. If you use...
It wasn't my meter so I am not sure, but I don't think that it had diode test function. Also, I had set it to measure resistance, and as I told you, I afterwards measured its voltage in that setting with another multimeter, and it was 2.92V, plus it works with 2x1.5V batteries so it can't...
I checked 2 multimeters that work with 2x1,5V batteries, and the maximum voltage (I measured it with another multimeter) that they produce when measuring big resistances is 2.9-3 V, as one would expect. So, normally they can do no harm to a human, as our body resistance is much more than 12 Ohms...
Thanks for your answers.
No, that didn't happen. I was just holding the electrodes, without pressing at them at all.
I am not really worried although it still feels a bit weird (ok, maybe it's just my idea). I understand that the current in such cases is just too small to cause anything...
Hi everybody,
I have a question concerning a "stupid" thing i did today. I found a electric multimeter (if it is called so- you know, the device that measures dc current, the resistance in Ohms, dc and rms of ac voltage...), and thought to measure my body resistance. I didn't even think that...
I wouldn't recommend looking at the Russell '1+1=2' proof, if you were referring to this specific proof. You may start by looking at what an axiomatic system is, what is truth in mathematics with regard to a specific set of axioms, study some basic Ecleidian Geometry, so that you can see how a...
The steps you take seem correct. A bit simpler way is to think of what you want to prove: (k+1)2<(k+1)! and by using equivalent relations to simplify it, like this for example:
(k+1)2<(k+1)!<=>
(k+1)(k+1)<k! (k+1)<=> *note k+1>0*
k+1<k!
We know that k2<k! so we just have to prove that...
From a book i have read in complex analysis, and from what i understand about the subject, I believe that we just define this equation. I mean, we define that e^{a+j \theta} = e^a{(cos \theta + jsin\theta )} . It's simply the definition for complex exponents. You can also reach this equation by...
I think we have done a circle here and reached my initial question. I have said that the above limit doesn't exist, and I get that you agree with that, but by using polar co-ordinates we get that it does exist and is equal to 0. And that was my question, why polar co-ordinates don't prove that...
I think that the problem may occur because of various definitions of things but in the case of the limit of the function, I believe (and hope) that there is a universal one... I have checked the definition of limit in three books (Calculus 1,2 and Complex Analysis) and in all of them the...
First of all, thanks for your answer.
If it is correct, then I think that we could prove that the limit doesn't exist, using only polar co-ordinates. And I will explain why this limit has sense in my opinion.
The function I mentioned is defined on RxR-{(x,0), x: real}. The point (0,0) is a...
First of all, thank you for your thorough answer.
From what you say in your post, I assume that I have misunderstood some things about functionals and generalised functions, partially due to the fact that I have read only a very brief introduction to functionals, and this coming from a book of...
Hi everybody,
I have just started reading some things about generalised functions, and i have some question. The source I am reading from is a book of partial differential equations so it's not a very formal introduction to generalized functions and functionals, but there are some basic...