Wow, replying to me 4 months later. Thats cool.
Anyway, I would argue that as 'our understanding' expands, what we understand also changes, and it can hardly be claimed that we are understanding the same thing pre and post expansion. If you make a claim about some elaborated kind of proof, you...
Thank you Fredrik, and Bacle2.
Definitions, and descriptions, I find to be extremely interesting. But that has little to do with math or physics so I'll avoid that conversation.
So I was working on a project related to sound harmonics. I had 12 harmonics/tones expressed as whole number fractions, all between 1 and 2, and I also wanted to have the reciprocals (multiplied into the range of 1 and 2), in the set of tones I was working with. So I had 15/8, and I wanted 16/15...
Hey guys,
I was working on something today and I was trying to formalize what I was doing, and I tried to write out:
M = { x | ( 2 / x ) \in M }
Then I thought about it and wondered whether this is allowed in set theory. Its not clear that there is anything in M at all, and thus its not...
Yeah I don't disagree, but I am getting at something else entirely. There is nothing about those proof that tells you they say anything about real physical objects like computers. I don't disagree that we can meaningfully demonstrate things about computers with math, but that's because I am the...
I believe you when you tell me a computer cannot be programmed to do those things, but its another thing entirely to say that a mathematical proof alone tells us what a computer can or cannot do.
Whalstib,
I think NumberNine was getting at something you arent appreciating. That, I suspect being, that dependent and independent have explicit statistical definitions, not conventional linguistic definitions.
Like, for example, I recently did a project at my university where I tried to...
Well... what makes something math?
"Mathematics" as I loosely understand the word, is used to refer to calculations and proofs, often about numbers.
Mathematics doesn't rely on the world for validity. The mathematical proposition '2+2=4' is not true because of some feature of the world we...
Random, as I understand it, means 'all possibilities with equal probabiliy'
So, flipping a coin is considered a random event, because in the scope of our problem we recognize two possibilities, heads and tails, and the probabilities of these possible events are equal. I am essentially...
I think I might have been a bit Brazen regarding some of my comments. But, maybe I can make a robust statement now that I've been thinking about this for a while.
1. Intutionism
'Intuitionism' kind of has two meanings. 'Intuitionism' started as a philosophy of mathematics, that being a body...
Yeah I am not sure.
I think its interesting how when symbolic logic was being invented, implication and negation were viewed as the basic components of logic. Today it seems like programmers view and or or and negation as basic parts.
Unlike philosophers or programmers, electronics people...
So I recently learned that you can derive all four of the propositional logic operators (~, V, &, →) from Nand alone.
As I have understood it, so long as you have negation, and one of the other operators, you can derive the rest. Like P → Q can be defined as ~P V Q.
However, I learned that...
Should we talk about this?
I think intuitionism is wrong. If we invent a kind of mathematical operation, then that operation, as its defined, leads to an outcome. Leading to that outcome makes it true. There is no way it cannot reach that outcome, least its not the same rule or operation to...