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Division into three parts or elements or a system based on three parts or elements.

Q: What is a trichotomy?

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The trichotomy law is essentially the law for ordering. Given any two real numbers, x and y, eitherx < y, orx = y, orx > y.

I think so. In x+iy, x and y are real numbers and have to be <0,0 or >0.

A "total order" of a set requires certain properties of the ordering function. For any A, B and C: Transitivity: A>B and B>C implies A>C Trichotomy: A>B or B>A or A=B These properties are true of the '>' operator meaning "greater than" when used to compare real numbers. This means that real numbers can be put in order by comparing them in pairs to see which is greater. Side note: without "Trichotomy", we would have a "partial order", where the order of the set would not be unique. For example, if the set were people, and '>' meant "is an ancestor of", then Transitivity would still be true, but Trichotomy would not. And there would be many ways to order a group of people so that descendants always came before ancestors.

A "total order" of a set requires certain properties of the ordering function. For any A, B and C: Transitivity: A>B and B>C implies A>C Trichotomy: A>B or B>A or A=B These properties are true of the '>' operator meaning "greater than" when used to compare real numbers. This means that real numbers can be put in order by comparing them in pairs to see which is greater. Side note: without "Trichotomy", we would have a "partial order", where the order of the set would not be unique. For example, if the set were people, and '>' meant "is an ancestor of", then Transitivity would still be true, but Trichotomy would not. And there would be many ways to order a group of people so that descendants always came before ancestors.

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The mantle is not exactly solid. It turns out that real life is a lot more complicated than the solid/liquid/gas trichotomy taught in elementary and secondary schools. For example, there are non-Newtonian fluids, and then there's the distinction between amorphous and crystalline solids, and supercritical fluids, and and and.The mantle is pretty rigid on human timescales (so "solid" isn't exactly wrong), but on geologic timescales it's better thought of as an extremely viscous fluid (so "liquid" isn't exactly wrong either).

Yes. Math is all about patterns. Every number larger than 1 will make the product larger than the original integer. I could describe this with a limit, but I'll hold off... As the multiplier gets closer to 1, the product gets closer to the original number. Until you hit 1, when it is equal. So if we look at numbers less than 1, we are force to conclude that the produce must be less than the original number, by trichotomy. Meaning there is no other choice: it can't be bigger or the same, so it must get smaller. Hope that clarifies.

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Answer 1This is not a trichotomy. Arab is an ethnicity, Jew is an ethno-religious marker, and Islam is a religion. Therefore a person can (in theory) be an "Arab Jew", a "Jewish Arab", an "Arab Muslim", a "Muslim Arab", or a "formerly Jewish Muslim". (Whether or not these terms are used is something else.) In terms of the Palestinians, they are exclusively Arab, ethnically and the majority are Muslim, but there are some Arab Christian Palestinians, Arab Druze Palestinians (although most Druze identify as Israelis, Lebanese, or Syrians), and Arab Bahai'i Palestinians.Answer 2the people of Palestine are a variety of Muslims and Christians. They used to live in harmony with the Jews under the British State (there was never a Muslim state that exclusively ruled Palestine).As soon as the Jewish areas received independence and Statehood, discord and war broke out.

A trichotomous system divides things into three categories, which can provide more nuance than a dichotomous system. However, a dichotomous system is often simpler and easier to understand, making it more practical for many applications. Additionally, dichotomous systems are commonly used in various fields and have proven to be effective.

The dimensions of man are built on one's definition of man. Man - by definition - is a tension filled unity that is capable of infinite possibilities which are both divine and demonic. If this definition is correct, then one must be able to define the unity from out of which come the infinite possibilities of man that are divine and demonic. Man is not a dichotomy or trichotomy wherein you can divide man into 2 - 3 parts. Man is tri-unity in His existence. Man is animated by what gives life to him and this animating principle is what defines those dimensions of man. Man is a three dimensional creature: biochemical, psycho-social, and ultimate or spiritual. The biochemical dimension is his body and what shapes and gives form to him in order for one to identify by others. The psychic-socio dimension is man's ability to relate, reflect and respond to self, others and God. The ultimate dimension of man is the one which is not acknowledge by secular disciplines but to their demise. The ultimate dimension is spiritual and is that by which man can transcend self and relate to those values, principles and persons of the spiritual world. It is meaningful to speak of man in these three dimensions. Man has life when at least 2 of the "three dimensions"- biochemical, psychic-socio, and ultimate of existence operate and function but the question as to the highest quality of life is whenever man has all three dimensions existing and functioning

This (If a>b and b>c then a>c) is an example of the transitive law or law of transitivity. A good treatment is in Chapter 1 of the classic textbook A Survey of Modern Algebra by G Birkhoff & S MacLane. My answer is a brief version of theirs. First we establish that we are are working in the type of algebraic structure called an ordered domain. Well-known examples are the integers and the real numbers. We assume we have elements a, b etc. and an operation +, such that a+b is an element of the domain. Fundamental properties (assumed as postulates) include that there is an element called zero (0) such that a+0=0, and that every element a has an inverse x such that a+x=0. The inverse of a is conventionally called -a. Also b+(-a) is conventionally written b-a.So far this is just a domain. We now define what we mean by an ordered domain. This is a domain in which some of the elements are said to be positive, with the following properties : (the addition principle) if a and b are positive, then a+b is positive; and (the law of trichotomy), for a given a, either a is positive, or a=0, or -a is positive. A relation > is now defined as follows : a>b if and only if a-b is positive.Having established the definitions and postulates we can now prove the result. If a>b and b>c, then by definition this means that a-b and b-c are positive. Now a-c=a+(-c) and (-b)+b=0, so a-c=a+0+(-c)=a+(-b)+b+(-c)=(a-b)+(b-c), which is the sum of two positive numbers and so is positive by the addition principle. We have proved a-c is positive, i.e. a>c as required.Note I have also used the associative law a+(b+c)=(a+b)+c which I forgot to mention!I hope the above isn't too heavy - but if a person asks the original question and doesn't just think "it's obvious" as many people would, I expect that person is probably interested in the fundamentals of mathematics!