Comments by "Pete Venuti" (@petevenuti7355) on "Is 1 a Prime Number?" video.

I like to see operations like adverbs, the definition being a description of the process, basically, am I wrong? In the specific case of 0 / 0 , would it be one zero or undefined? It largely depends on your definitions of division and zero.. what are the generally accepted definitions? And I don't believe in the idea of dividing by 0 equaling every number because even if you had an infinite number of zero say in the number five you still would never get to that five so it makes no sense, but if you divide zero by zero you still got one zero in that zero so it's equal to one. On the other hand if you considered division a multi-step process, then dividing anything by zero even zero would be a do nothing function because it would be zero steps, and what do you return from a do nothing function? Zero, the starting number, or is it just meaningless? From the videos of yours I've watched so far I find your logic impeccable, and over the last 50 years I have watched definitions changed so I am greatly looking forward to seeing how you can logically justify or create appropriate definitions of these fundamental principles. Personally I believe math definitions should enable a self-consistent logical structure across the whole that correlates with reality, anything that deviates from that ideal could not be math.
1
@rmsgrey if division is defined as recursive subtraction, then we stop at zero in one step so answer would be one, if we define ass recursive adding of inverse (15/3= 1/3+1/3.. fifteen times) then Wouldn't 0/0 be 0? I didn't get to point this out in the live stream, but if one is defined as a set of one empty set isn't one empty set 0 just as prime as one? If you think of something times zero as a do nothing function and that's why it returns zero , then zero is not in other numbers like a factor ... Sorry it's hard to describe, I'm hoping someone else can take the ball following the logic.
1
@rmsgrey that's the best answer I've ever gotten! Going negative with recursive subtraction, I don't know why that never occurred to me 🤔, good point! Ultimately what I'm asking is.. What is the concise definition of division? Then I can see how it works, where it breaks , and think about how the undefined can be defined without breaking the rest of math. I guess I'll just have to wait for the next video.😁 The concept of the empty set being the building block of one does seem to make 0 a factor of everything, that deeply appeals to me on a religious/philosophical level... Still , must stick to logic to do math.
1
@angelmendez-rivera351 I'm trying to make dinner right now , but upon seeing this , I had to give you an immense thank you for your superlative thoughtful reply! I'm going to have to go over it later when I'm less distracted.. But what I did manage to read sofar leads me to believe you might be able to answer a completely unrelated question.. Is there such a thing as a ternary operation that can't be broken down into binary operations.. For instance, a function that takes three values , is dependent on all three , but reaching the output of this function could never be accomplished say using an equivalent transformation matrix......speaking of things computers will never be able to do.... Also I'm having a little trouble wrapping my head around how operations cannot be compared to or defined as algorithms... It's like, then,. how do you do math? What is an operation then? It must involve action, yes? Like a verb.. I'll get back to you , or I'm going to ruin dinner...
1
@angelmendez-rivera351 maybe there's a difference between us in the way we assign meaning to those variables we call words. Mostly I'm referring to the word algorithm. I understand what you're trying to say about identities and how that is part of the definition of an operation (that's why I chose the word adverb instead of verb in my analogy) what I am not getting is how any operation, is not , at least in some way, an algorithm. Because at its most basic both are something you do with a definition of how to do. I can see why my computer analogies would cause a problem...
1
@angelmendez-rivera351 and again, thank you!
1
@angelmendez-rivera351 between you and the rmsgreay any hubris I had took a sledge hammer.. between command of logic, fluidity of passing between levels of abstraction not to mention vocabulary I've never heard before... it feels good to be a party to this dialogue, very educational. Also I feel completely jipped by the educational system... Yet to get back on topic... Personally in my mind any linear algebra has that one input one output property and that's what linear means in that context. I don't believe you are also saying that a function has to be linear to be a function were you? I'm assuming that only needs to be the case in the description of the definition of the simple binary functions we are discussing being division multiplication and what they're built from, I believe you're only saying that those specifically have to be linear , correct? What would be your opinion on giving 0/0 it's own symbol, much like the numeral " i " , (essentially making it its own object outside of the systems you guys were discussing that I don't know the vocabulary for) even if it won't allow for a conceptual definition (like i) it would at least make errors glaringly obvious. I think I'm seeing what you're trying to explain to me, your separating the concept of what these relationships are from the mechanism of how they are calculated. (separating the adjective from the verb in an adverb?) They're very intimately related so this is difficult. I never was and would never deny the concept of infinity, and I don't think you were saying I was, I think you were just saying that some of the things I was saying would point to that conclusion but in explaining that to me it sounded like you're denying the concept of "nothing" or by saying "nothing doesn't exist" or did you just mean in the sense that that's what nothing is by definition, something, everything, that doesn't exist..?
1
@angelmendez-rivera351 well formed formula in the language of the theory .. personally that is my definition of an algorithm, I wasn't limiting myself to just the realm of computability. I guess you assumed I took computer science (*true*). I'm not sure where my sense of 'linear' came from, at least we both agree on what we respectively meant. I've never taken linear algebra, my first exposure was watching Lenard Susskind videos, and the way he explained some things made quite a few ideas click, from representing some calculus as matrixes to how neural network software manages Fourier transforms.. even though he was talking about the field quantum mechanics.. Our talk has brought a lot into focus for me too.(and a lot of further reading) it's amazing anyone can communicate sometimes given how inconcise english can be. Thanks for your patience helping me understand the language of your field. Are you a professor?
1
@rmsgrey seems as if any proper function can ,( and please excuse this layman's potential bludgeoning of terminology ) , can through the proper application of derivatives, matrixes and other forms of transformation make most any function appear as a straight line.. just as one might be able to relate my earlier use of the word to the mathematically correct use of "linear" . I concede that the proceeding is likely only true within limits, I just haven't gone that route in my education to know what those are. so, I'm just saying, "looks like" from the perspective of what I've seen.
1
@rmsgrey I was just pointing out how significant it is that there can be such widely different meanings of the same word between people even speaking the same language. I meant linear to denote the one to one or many to one relationship defining a function , you meant linear essentially as a line in a coordinate system and Angel I believe originally meant it in the strictest sense of linear algebra. There was also some ambiguity and difference between the way I meant algorithm and the way he thought I meant algorithm from the way he would mean algorithm.. I did get what I was mainly fishing for, I just didn't know enough before to know what to ask. Such as how to get some of the definitions as they're commonly agreed upon by mathematicians for our current system of math Which are the standard axioms (Angel mentioned two names I got to go back and look) and what they imply. I haven't looked yet but I doubt they include methods on how to do operations as part of their definition. Not even sure if necessary as long as the axioms are not contradicted. I'm Still having trouble separating the conceptualization of a functional relationship from the process of doing one. (That's what she said 😜) I want to read about some of the things you guys were talking about before I ask any more questions, see if I can figure out the " how to proceed" part of their meanings to extend the definitions for myself for practical use in which there is apparently some flexibility as long as the axioms aren't contradicted. (I'm trying hard not to use the word algorithm again, because apparently it implies limiting oneself only to the process of the computable) Then maybe I can build myself back up to the first grade level and strengthen my foundations.🤓
1
@angelmendez-rivera351 I ment "function" in a broad sence , program , transform or relationship.. sorry if I introduced ambiguity. Diagonal argument, sounds good, I'll look, thx. Still have to look up irreducible n-ary's though 😊 Computer science and mathematics started out quite mingled and have since diverged , like compare organic chemists, even biologist to someone who does genetic engineering , it has diverged a lot over the decades. Know of Gerald Sussman? He's old enough to remember when the fields overlapped completely and likely more familiar with both then the 3 of us, definitely me..
1