Interesting and Humour - page 4870
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assumption, axiom, not no, but is, false, true.....
Just imagine that 0 and infinity are part of our objective reality.
That's pretty much how we live our lives. With these assumptions. Just forgetting what is true and what is an assumption is fraught with sisyphean sophistry)
In modern mathematics, it is common to start with sets rather than numbers. Integers are introduced as classes of finite sets of the same power. Zero is the power of an empty set.
This is not the only way of introducing numbers - there are much crazier ones.)
Who's to say) We've got apples so far) Yes, no, how many grams)
This is exactly where it's not. These are proven states for reality. And complex and irrational. And zero is not proven as a state. As a concept it is confused with the Boolean False. And then on the axiom begin to do philosophy of miracles) Where it is very difficult to separate sophistry from reality. Well, no one has done away with the hysteresis of logic either. The barbarian is a good example.
I mean, 0 apples you can't, but -5 apples you can?
Who's to say) We have apples so far) Yes, no, how many grams).
If we talk about a mathematical model, it is not just "apples", but "some set of apples") which has a defined power, in the case of finite sets, called a number (of elements of the set).
Then comes algebra, which is used to introduce negative and rational numbers. Real numbers have to be introduced on the basis of rational ones in the framework of matan (dedekind sections, for instance). If the constructive (algorithmic) approach is used, however, it is not possible to get all the real numbers - only a countable number of them.
I.e., 0 apples are not allowed, but -5 apples are?
Historically, negative numbers have been explained as being in debt. Consequently, zero is when no one owes anyone anything)
First you have to count the particles of the apples, and then it's time to move on to counting the apples themselves. One should also take into account that apples may be -5.))
How to dive deep into particles? "The electron is as inexhaustible as the atom. Nature is infinite." Lenin
How to dive deep into particles? "The electron is as inexhaustible as the atom. Nature is infinite." Lenin
Nature is infinite, but it's still not clear with apples.)
So you can't have 0 apples, but you can have -5 apples?
Of course you can. Only the entities are different.
-5 is debt. 0 is boolean negation. And 5 is apples))))))
If a mathematical model is referred to, it is not just "apples", but "some set of apples") which has a defined power, in the case of finite sets, called the number (of elements of the set).
Then comes algebra, which is used to introduce negative and rational numbers. Real numbers have to be introduced on the basis of rational ones in the framework of matan (dedekind sections, for instance). If you use the constructive (algorithmic) approach, you can't get all the real numbers - only a countable number of them.
All true, BUT how difficult to understand it is.... And there is not much practical use for most. But it's an interesting topic...
yupd. It is not difficult to understand, but difficult to explain clearly to those who do not understand)))