ahmet

hi, I have not clearly understood what kind of message you want to transmit to us but as the title is very clear and its color is very obvious, while I would not like to make any explanation about my own idea in the current position,I would definitely express one woman who has far relation with me; she says: "why someone says to other ones marking or calling them as 'stupid' ? did they create them?" Clarification: that woman intented to express that it would not be convenient to call anyone as "stupid". I can also consider that this would always be an insulting word. (assume please someone head to you by calling you with this word,the implication is also awful.) however, under this instructions we can also not call someone even if someone has had disease (mental ilnesses) because (although this approach will potentially include relative idea) that woman also expressed this in the content "you or people did not create that one, so you/they cannot call him as 'stupid' " and illness is generally not in your hand some keywords: ethics ,aesthetics,manner, human rights.

pink winds from russia ... wwuuuuuuu :) :) :) https://www.youtube.com/watch?v=wbSxTL_Fppw&list=RDy_ONldN0pCE&index=9

as it explained we will accept [math] -\infty,\infty [/math] as points. Thus this is not a type of discontinuity. (but if any case be occured like right limit and left limit are different points then this will be discontinuity.) and arc means inverse trygonometric functions (e.g. arcsin(x) ,arccos(2x), etc)

hi, I do not remember whether any function given in this category has had discontinuoum point. But with one notation: [math] -\infty, \infty [/math] are accepted as points. (This is real analysis) thus if any point accepts its limit one of these points,then this is not a problem. (however, one point cannot accept both of these points as limit point ,because this will be accepted as discontinuoum) elementary functions : LAPTE L: logaritmic A: arc P: polynomic T: trygnometric E: exponential. thanks.

graphs yes. To me,although during maths BSc program no one mentioned ( in spite of other very strict contexts ), (because that example is too simple to me ( 1= radius circle) I almost always was thinking it would not be accepted even as a function , because for instance when we draw the graph, it is possible to find two elements which their values (under the functions's rule) are same but, are not equal. ( here if x= sint ,y = cost ,e.g: for t=45 degree , [math] x^2+y^2=1 [/math] is being satisfied but there when the angle is 135 degree , y value is again same thus this should not be accepted as a function in fact) meanwhile, you might be right, because as I remember, the curves and functions are slightly different (probably there was continuoum between the definitions or homeomorphism,I do not remember well,sorry for that but can scan the documents if you want,or you might be better on this issue) the definition of function is simply f: A ---> B , every x element of A should have a value in B , and when [math] x_1=x_2 [/math] (these are element of A) and [math]f(x_1)=f(x_2)[/math] this is compulsory. E xamplifed above for circle. (circle equation is not a function) but if you specifically define it between 90-180 and 0-270 ,then well this will be accepted as a function. (but the domain set and value sets will be changed as you can predict)

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pahahaha never mind such things. mmm, listening musics gives more pleasure than imaging such things peheh A recommendation: I suggest that you visit Antalya's The Land Of Legends or vialand in istanbul or any else a good theme park rather than imaging such things, I guarantee more pleasure.

hi, can we conclude/say that all of elementary functions (that consisted of just one term) were simple curve elementary functions : *trygonometric (cannot consist of more than one term) *logaritmic (cannot contain more than one term) * polynomic (this category can consist of just one term and can be divided to two subcategories : 1) with odd number degree 2) even number degree (e.g. [math] f(x)= x^{3}, g(x)=x^{4} [/math] )) * inverse trygonometric functions (cannot be more than one term) * exponential functions (should contain just one term) All these functions should be simple curve ,could you confirm this information please? clarification: the criterion given in the paranthesis are in fact ,all equivalent and means this for instance : trygonometric functions cannot be defined like this one: [math]f(x)= cos(x) + cos(tx) [/math] t ∈ R constant number) or this one [math]f(x)=sin(x)+cos(x)[/math] for exponential functions for instance none of these are acceptable [math] f(x)=e^{x}+e^{5x} , g(x)= e^{x}+5^{x}[/math] and so on. futhermore just one type of these functions are claimed not the mixture of them (e.g. this is not an issue: [math]f(x)= cos(x)+x^{4} [/math] )

oh my gosh! I am full with energy! is this caused by eating walnuts , hahahahaahaha oh natural , natural, natural , one another nice musics even if I do not know what "chameleon" means.

it seems like a POPular wind is blowing from russia.

I listen only POPular musics full energy!

oh my gosh! I can't move to anywhere it is because of covid - 19. may I ask something more while trying to make my boring times go away 1) does youtube pay fee just regarding the count of watching (assume please ads turned on)? 2) what happens if the language option is changable (in fact this is the same question with previous one) A notation: I have detected many music videos ,that seem like some unqualified productions, however, they are watched too many times.

music , music , music

thnak you for suggestion,I had better read the books you provided here and similar books. Because I hope I shall see the proofs of claims (e.g. if this is regular continuous then ...(it will show me))