syzarian

[1] https://www.sfchronicle.com/crime/article/Is-the-San-Francis...

[2] https://www.finder.com/uk/police-statistics

As usual in field theory, the convention to consider p / q as an abbreviation for p · q−1 was used in subsequent work on meadows (see e.g. [2,5]). This convention is no longer satisfactory if partial variants of meadows are con- sidered too, as is demonstrated in [3].

So, as I’ve stated many times, I talked about convention and indicated you can use whatever terms you want. In the paper quoted above they acknowledge what the convention is. That is that division is multiplication by the inverse. They are arguing that it is worthwhile in this new algebraic object to change the usual notion a bit. If people agree to a new usage of the word division then definitions will change accordingly. None of this is pertinent to the spirit of the original question given the context under which it was asked. All of this is highly technical.

Definitions and notions change as new mathematics is created (discovered?). This happens all the time. All you have to do is convince other mathematicians to go along with it.

https://arxiv.org/pdf/0909.2088.pdf

EDIT: Regarding what you wrote in your other comment: The analogy is not apt in my opinion. It’s hard to say zero can’t exist because the nonzero…. The moment you say nonzero means it does exist. I think a better way to look at the situation is:

I have an object that is a group under a binary operation f. There is another natural binary operation on that object that operates with f in a consistent way. That operation doesn’t form a group but if I add a symbol to my set and give these rules then both operations interact in a consistent, natural way. I get a group under the new symbol with the second operation while preserving the group under the first operation minus the new symbol.

With extended complex numbers you don’t quite preserve the structures or properties that one normally wants so I’d say it isn’t true division. It is division like.

Edit: The nation as a whole has shifted very much rightward the last 50 years. Instead of saying Republicans I should maybe say “right leaning politics”.

1. Not give an opponent an easy way to attack you that requires the masses to employ nuanced reasoning to understand why that attack is wrong.

2. Say things to your base to keep them voting for you even though you have no intention of implementing those policies.

The answer given to the person who asked the original question was the correct one. You can’t do it because doing so would break consistency and that is of paramount importance when doing new things in mathematics. There are agreed upon usages of terms and symbols in mathematics. Why call something division in the true sense of the word when it breaks the conventional usage of what that term means? But, also, why invent a new symbol to denote what is analogous to division? So we abuse notation. This is done all the time. So on the one had we’ll say to calculus 1 students 1/infinity is 0 but also say infinity is not a number. Things are done for convenience but when asked, “Is this really division?” the answer is no.

Of course you can redefine all terms you desire and say things like: A circle can be squared, I just mean something different when I say circle than when you say it. But why do that? All of this is my opinion. You disagree and that is ok.

EDIT: It is definitely not a dumb idea as you suggest. Many counties have sensible policies on this issue and yet they manage to trudge along without much trouble. As I said it is OK to advocate for pay-as-you-use government so long as people like you don’t pay for your negative externalities too often.

In math often times the answer we give depends on the knowledge of the person asking the question. For instance we tell calculus 1 students 1/x is not continuous as a function from R-{0} to R. Of course in the standard induced topology it is a continuous function but explaining this to calculus 1 students would be very difficult.

https://math.stackexchange.com/a/2524779

I know. Please don’t become a teacher.

If something doesn’t behave like 0 in a ring or other algebraic structure then using that label is confusing and simply not done. You are free to use any symbol you want but mathematics is a human endeavor and as such communication is important. Using the symbol 0 signifies something to those with mathematical training. Zero can’t have an multiplicative inverse because anything you call 0 that has an multiplicative inverse makes it behave like something other than zero. So no one would use 0 to describe such an element. In a ring, or abelian group, the symbol 0 is reserved for the additive identity element.

Similarly, I could say snkwoo is what most people call a chair. A grammarian would say there is no word snkwoo even though I just defined it.

Your original comment was wrong and bad. Instead of just admitting it or moving on you’ve decided to double down and make another bad comment.

In a ring the elements form a group under addition and thus every element has an additive inverse. The additive identity element, let’s call it e, has the property that ea = e and ae = e. For this reason we use 0 instead of e. In a nontrivial ring 0 can’t have a multiplicative inverse because if it did then every element would be equal to the multiplicative identity (which is unique).

Most questions asked by beginners in an area are “stupid” and few as insightful as this one. I’ve taught mathematics at a community college for 20 years and I would be delighted to have been asked this. Usually questions are mundane like, “Why did you add x to both sides?”. Here the person is trying to understand what mathematicians do, what the basis of expanding a number system really involves. This is a fantastic question.

Peoples’ curiosity ought not be labeled as stupid.

You are being deliberately daft. Obviously not. The situations aren’t comparable.

Legislators should not be expelled as a result of nonviolent civil disobedience. It is true that there are rules for expulsion and those rules were followed but when things like this are used in an unprecedented way and the normal way legislative bodies function gets upended suddenly it’s a bad sign. Democrats have not kept up with the new political reality.

What is interesting about your comment is that I made no appeal to authority. I did not quote anyone or make any references to an authority. What I did was to ask JuJu to consider something and to state what I think.

What’s ironic about your comment is that JuJu did make an appeal to an authority.

EDIT: You believe 1+1 equals 2. I doubt you know how to prove this rigorously. Your belief is based on an appeal to authority. Have you independently verified that electrons exist? Or that the moon is a little more than one light second away? Have you ever supplied links to an article to support a position you have?

A baseless claim says much about the person making it. A claim that is well reasoned and supported by the facts says very little about the person making it.

If I say: The IQ of blacks in the U.S. is on average lower than that of whites. that says nothing about my ideology. If I say: Black people are stupid. that says much about my ideology.

Making a claim that is well reasoned and substantiated by the known facts says that the person making the claim reasoned it well and had facts that supported that reasoning and they possessed the vocabulary and permissiveness to discuss those ideas. One can not infer a person’s ideology from such a claim. Of course biases and experience play a role in these things but looking from the outside you can’t say of well reasoned claims: personal imposition. That is too strong of a conclusion.

This gives me the impression that VoodooJuJu thinks the historian had an ideological agenda and was making a square be a circle so to speak. If the historians claims are not baseless then how can personal imposition be an apt description?

I agree with what you wrote but I think your edit is wrong. VoodooJuJu didn’t use the word baseless but I think that is the essence of their claim. How can the historian’s claim be an insight into today’s culture, views, and lives if the claim is well reasoned and substantiated by the known facts? A claim that is well reasoned and substantiated by known facts is a claim that could be made by anyone whose language has words for what we call transvestism, gender fluidity, and androgyny. It seems to me at most, with a claim that is well reasoned and substantiated by known facts, one can only infer the level of permissiveness that experts had to discuss such topics.

An intellectually honest response to the link supplied by weakfish would be to question why defender of gender fluidity is the right description while acknowledging that this is new information and that your initial response was wrong. That the description defender of gender fluidity might have some merit to it but you remain skeptical and would like to learn more about why people use this description.

Consider the possibility that experts who study this stuff came to the conclusion because that is where the evidence lead them. That if you had expertise in this area that you too would see this as at least extremely plausible.