This is just humorous thought of mine…
If we have a “collection” where isn’t anything, is it a collection? If someone has got 100 books, the person has a collection of 100 books. But if a person hasn’t got books at all, does the person have a collection of books? No.
So, is the empty set as such a set? A collection where is nothing isn’t a collection.
But is it an empty collection? But is an empty collection a collection at all? 🙂
I’ve been reading e-book ”Introduction to Mathematical Philosophy” originally written by Bertrand Russell and published in the year 1901.
Among other interesting thoughts Russell gives thought to the definition of a number. This is something very interesting; I’ve been thinking myself strange things about number zero. Can zero be considered as a whole number? It doesn’t describe anything existing as whole. If the number of something is zero, this something doesn’t exist at all in somewhere, particularly not as whole.
As to definition of number, Russell discusses about classes. From an old Finnish book that discusses university level algebra, I recently learned the definition of zero as a class. In Russell’s book zero is defined as a class in slightly different way: Russell doesn’t say anything about the empty set, instead he mentions ”null-class”. I think I will read this part of the book over and over again.
This is something fascinating…
Hopefully you got interested in this great book:
This is perhaps funny sounding concept I came up… In sacred geometry everything is defined through geometry; what is post apocalyptic sacred geometry?
With the post apocalyptic sacred geometry I refer to imaginary new world, where geometry defines the ”rules” of this world; what is changed now?
In post apocalyptic world the geometry on which everything is based, makes it impossible to feel pain, get hurt or harm anyone or anything. Some kind of imaginary sacred paradise through geometry that doesn’t allow anything bad or evil; these things don’t exist anymore and every possibility to do anything is good; and from good ”spirit” of every deed arises more good; one good thing is eventually more than just one thing, perhaps fractal-alike thing…
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In this imaginary world immortality is something considered self-evident; nothing can harm anyone in anyway, because the nature of post apocalyptic sacred geometry.
Through sacred fractals one thing is endlessly interesting, there absolutely doesn’t exist possibility to get bored, which on the other hand is impossible through new post apocalyptic sacred geometry.
Not even smoking can harm anyone’s health in anyway in this imaginary world of post apocalyptic sacred geometry. 🙂
In multiplying one (1) is neutral element: a * 1 = a. For example, 7 * 1 = 7. Number one keeps the identity of a number, which includes a number being even or uneven. But what about zero (0)?
0 * 1 = 0. Does one keep the identity of zero or does zero keep the identity of its own? The property of this identity is ”zeroing” property: a * 0 = 0, were a whatever real number, including one and on the other hand zero.
In case -2 * 0, zero takes the whole identity of number -2: The number being negative and even; as a result we get ”just” zero. Similar happens in 2 * 0 = 0.
“Unique Sphere Shows Standing Out”
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My two cents: Zero ”zeroes” any number except itself. It ”zeroes” the whole identity – including a number being even or uneven – of any number except from itself; in case 0 * 0 = 0 zero keeps the identity of its own, it doesn’t ”zero” itself, which reflects the identity of zero itself, how it is neutral in a deep sense and meaning.
Mathematical philosophically zero refers to none, there isn’t something at all. Still, zero refers different than nothing. As I’ve written before emptyness (”zero”) can be created, nothing can’t be created; it is from which the creation begins.
Let us assume, that we have two (2) coins. It’s even amount of coins. Let’s give one coin to a poor beggar. Now we have only one coin, uneven amount of coins. We’ll give that coin to a poor beggar too. Now we have no coins at all, the number of coins we have is zero. Do we have still again even number of coins, as we have zero amount of coins? I mean, we don’t have coins left at all!
The coins we had were in a wallet and the two coins were all we had there; now the wallet is empty. Is emptyness even or uneven? Or are we speaking now about different matter?
As far as I can see, if the number of something is different than zero, there must exist something, somehow. This number is even or uneven.
So, number being even or uneven, philosophically would refer to existence; something must somehow exist, that is, the number of something is different than zero. This amount can be negative or positive, even or uneven, but not zero.
But if something doesn’t exist, the amount of this something is zero, that isn’t even or uneven, as stated before. If the “number of something” is even or uneven, something must exist, somehow.
Technically one test to determine, that is a number even, is to divide the number to be tested by 2; if reminder is zero, the number is even. This test is suspicious to zero from two (2) reasons:
- 0 / a = 0 anyway were the number a whatever real number (except zero)
- Two (2) is greater than zero by its absolute value (philosophical mathematical problem)
My two cents: Zero is neutral element in addition and one of its properties is, particularly philosophically, that as to being even or uneven, it is neutral.
(As a sidenote something came into my mind from section 2 above: Is number one (1) somehow fundamentally uneven in natural numbers set?)
I want to share some important thoughts from a book from Viktor E. Frankl. The Finnish name of the book is Tiedostamaton jumala. The original name of the book is Der unbewusste Gott.
There seems to be two versions of this book in English 1) The subconscious god and 2) Man’s search for the ultimate meaning.
Among other things Frankl discusses when a person’s choice of a partner is really the choice of love.
”Id” refers to sexual instinct (I hope I use right translation), ego refers to that something that is ”me” for a person, that ”mystical” I who thinks and feels. Super ego refers to conscience.
Frankl explains that as long as ”id” determines the choice of a partner, the choice is not the choice of love. I think this kind of choice could be described more like choice of lust.
When ego is free from ”id” and makes its own choice, only then the choice is really choice of love when the context is choosing a partner to love. To me this is one of the most important thoughts of the book.
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Sometimes I’ve wondered when in James Bond movies people often complains about 007’s ego, that should it sometimes be 007’s ”id” they should be complaining about… 🙂
It seems that I have forgotten lots of things recently. Luckily I haven’t forgotten anything in oven while making food… Even in this short blog post I had to use dictionary a lot.. 🙂
Recently I started to think, that have I forgotten what kind of person is a strong person. Sometimes in my experience nowadays we live somehow in a heartless weak world. Is it then easy to be strong here? No.
One good characteristic of a strong person is balance in a wide sense. For instance, one characteristic of strength is restrain, what represents balanced person capable of sensible consideration and judgement. A strong person doesn’t easily get upset or angry; one should remember, that hate blinds and makes eventually weak. The ”power” of hatred is only a delusion.
To grow up a strong person is hard and to keep oneself strong is hard; in practice one must have courage to be weak and face the truth: One must face oneself, own weaknesses and win them in order to grow a strong person.
One problem may be blindness to own weaknesses; one may believe that something that in fact represents weakness, represents strength.
If one doesn’t have courage to face oneself — the whole truth about oneself — one doesn’t really have courage to face anyone else either in a true way; one doesn’t really see other people. This may cause one to harden oneself and become ”tough”, what in practice means cowardice. At least eventually.
How could love in this case be strong, which represents real strength. True strength.
We all have inner demons called hate and fear among others, that we must conquer. Perhaps someday we will see a world without wars, when everyone has defeated their own inner demons, particularly fears and hatred.
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In big heart there is room enough to pain too, so that pain or fears can’t suffocate the starting sparks of love. Eventually love will melt all the pain when it gets its chance. Perhaps I’m only dreaming… Though, I hope not.