I was wondering if there were any well-documented instances of female mathematicians’ work being overlooked/dismissed, and credit being given to male mathematicians who came along later and built on their work or independently replicated their results.
I would also be interested in hearing about any female mathematicians whose work is not commensurate with their recognition in the field today. (I recognize that this may be true for most, but I’m particularly interested in mathematicians that are not among those usually mentioned in this discussion e.g. Noether, Kovalevskaya.)
I have a working number theory of my own, but I lack the background to criticize it or place it in the proper context. Advice is welcome. I’ve thought about this for a long time, and I’d like to understand it completely. I suspect it falls under some other theory, and I would like to know what it is so I can learn about it.
I propose defining the natural numbers using systematic conjunct statements of identity and non-identity, and nothing else.Tell me where my system fails.
The number one is defined as the identity relationship, or the condition of being the self-same, as in, Batman and Bruce Wayne are “one”. They are not only the same, but they are the self same. A statement that affirms the identity relationship is the same as a statement that says it is of number one.
The next natural number is defined by a conjunct statement, in which one must make the first type of statement, make the first type of statement again, and most importantly, make a third statement that there is a non-identity between the first two. For example, if you say Bruce Wayne and Batman are two people, then the contradiction of that would be the contradiction of that third statement, (the statement of non-identity). In other words, the contradiction is the statement that there is an identity relationship between them, that is, the contradiction of the statement that there is a non-identity relationship. Without the third statement, two is no different than one.
What that means is that every natural number has to be defined with a conjunct statement that includes a certain (great) number of conjunct statements. To completely define a number n, or merely to state with certainty that a certain thing is of number n, one must make (n(n+1))/2 statements (n + n-1 + n-2…) So when you state “I have $20” you are actually making 210 separate conjunct statements. (Not only that, but the power system of a standard base number system is also a shortcut method of naming numbers, but I’ll ignore that for now).
When one says there are n things, they make reference to a vast number of implicit statements that are required in order to for it to be unambiguous. Because numbers are so handy, we neglect to even consider that these implicit statements are necessary. But without them, two and three are no different than a million.
From that perspective, it is easy to resolve the seeming paradox of numbers- that they are both invented by people, and yet their properties are not always known to people.
Proceeding from this definition of numbers, I can define operations of arithmetic. I can show why, for example, some operations delete information, and others require input of information. For example, we say 4X4= 16, but in truth, they are only equal in one way, not in every way, because there are more bits on one side than the other, which is why, given factors, I can name a product, but given a product, I cannot name the factors. Using my system, I can not only see why information has to be deleted, or supplied, I can count _how much _ information.
When I read other established number theories, they appear to have many equivalences to mine. But it seems to me that mine avoids all of the difficulties of theirs. But then, my background is pretty weak, so I was hoping someone could steer me in the right direction. Any advice is appreciated.
I was researching inductive sequences recently, and I came across how to find the limit
The particular recurrence relationship was: U(n+1) = 2/Un +9
I found it to have 2 limits by solving it as a quadratic where U(n+1) = Un, because it is a converging sequence.
The limits were (9±√89)/2
By simple reiterative process, I was able to see how the positive limit was reached. However, there was only 1 number (9-√89)/2 that gave the negative limit, and I think that it’s a trivial solution, given that it is the limit itself.
My question is, are there any negative numbers that when iterated in this sequence, give the negative limit of the sequence?