Un fel de concluzie la postarile despre numere
- programein
- May 30
- 2 min read
Pentru ca nu stiu exact cum sa sintetizez mai bine aceste postari, mi-am amintit ca am facut un comentariu la o postare pe internet, facuta de catre o doamna fizician. Desi postarea era despre fizica, atingea o latura matematica, asa numita intuitionist mathematics(in limba engleza), care se apropia de subiectul numerelor. De fapt era vorba despre propunerea unui fizician de a revizui metoda matematica din studiul fizicii, se atingea si problemaa infinitatii si a numerelor reale. Si pentru ca mi s-a parut subiectul apropiat, am scris acest comentariu, pe care am sa-l atasez mai jos. Poate ca subiectul de fizica ar fi fost interesant, dar pentru mine a fost declicul pentru acest comentariu-sinteza
Comentariul meu
In fact, if we redefine real numbers in a different way, we arrive at the conclusion that we never actually operate with real numbers (classical operations using a finite-step algorithm). I have a blog as an amateur mathematician where I explain this. I don’t know much about physics and I don’t claim to, and maybe this idea isn’t helpful in mathematics either—I haven’t had time to delve deeper into it. If anyone is curious, I could share a link here. Unfortunately, it’s not in English yet, but it can be translated somehow automatic
Raspunsul meu la comentariul meu, pentru ca nu am avut nici un alt raspuns
Some clarifications regarding the aforementioned redefinition. Real numbers become necessary when natural numbers, integers, and some rational numbers cannot represent certain results of arithmetic operations, such as 1/3. Thus, infinite representations become necessary, but classical operations with a finite number of steps cannot be applied to these infinite representations.
Operations such as (1/3)×3=1 were then postulated without operating directly on 1/3, relying instead on the properties of operations within natural numbers (integers and some rational numbers). However, these operations on infinite numbers, just like the concept of taking a limit, are postulates (axioms). Similarly, the equality 1=0.(9) is also an axiom.
Thus, if we exclude natural numbers, integers, and some rational numbers from the set of real numbers, we are left with a set of truly real numbers (infinitely represented), which we could call the "nucleus." The real numbers (as currently defined) are essentially the extended real numbers, where we take the "nucleus" of real numbers and add natural numbers, integers, and partially rational numbers to obtain the extended real numbers. What I mean to say is that within the "nucleus" of real numbers, arithmetic operations cannot be performed using finite-step algorithms—only after their axiomatization. Of course, these are personal opinions from an amateur mathematician and do not change anything in mathematics.
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