Can someone prove 1 + 1 3
Forum: Offtopic 1 + 1 = 2 is an unprovable mathematical axiom?
I once heard that you can't prove this mathematically. I do not understand that completely. I can personally prove to myself that 1 + 1 = 2. Can someone explain why it cannot be proven mathematically? Thank you thank you! Cheers
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According to Wikipedia, an axiom is a basic statement that is accepted without evidence, which settles your question :)
The square root of 4 is 2 but could also be -2, or not; -} Reason: (-2) x (-2) = 4
This is a statement that at some point was assumed to be true. You can't prove it, it's just like that. One can also define mathematical systems in which 1 + 1 is not 2. Something like that was done with parallels, for example, defined a system in which parallels intersect. Of course, you can't imagine that.
> but a simplification ... I have to remember the next time I go shopping at aldi :-)))))
7 = 5 + 2 | Expand with (7-5) 7 (7-5) = (5 + 2) (7-5) | Dissolve bracket 49-35 = 35-25-10 + 14 | - 14 49-35-14 = 35-25-10 | Factor 7 (7-5-2) = 5 (7-5-2) | Shortening of the same sizes (7-5-2) 7 = 5 ???? great is not it... ;-))
Okay now I know more. Thank you thank you 7 (7-5-2) = 5 (7-5-2) | Shortening away from the same sizes Here you divide by 0!
Helmi_7 wrote:> The square root of 4 is 2 but could also be -2, or not; -} >> Reason: (-2) x (-2) = 4 Well recognized. Take a look at complex calculation, then you will also find zeros: D edit: well then thanks for the hint :)
It is not a question of whether it is PROVEN or not. Can you prove that a goal scored from the offside doesn't count? Yes. By looking up the official football rules. Can you prove that these rules are correct? No. There are rules. You have set it up and you stick to it. Because it's functional and makes the game more interesting. So it is with axioms. There are (game) rules. Stick to it when you do math and you will find that the rules are fit for purpose in the sense that math is a good tool for understanding many things in the real world. Can you prove that 1 + 1 = 2? Why? Because you put an apple next to an apple and then you have two? No, you have only proven that this axiom is obviously useful. The math with its rules will help you deal with apples.
... I see exactly the same as Simon. Perhaps the following as a supplement: if you take the Peano axioms as a basis, each number has exactly one successor (whereby, of course, a start must be made somewhere, e.g. at 0 or 1). How the respective successor is called and with which symbol it is written is not defined. Whether we call the successor of the first natural number two, two, deux, or something else is another question. This does not mean how we symbolize numbers, e.g. with "2", "II", two lines on the beer mat, ... Oh yes, the Peanoo axioms are getting a bit old - today the Zermelo- Fraenkel set theory "hip".
> No mathematical proof, but a simplification ... In your pdf, the exponent n is missing in the denominator at the bottom right. (Must be called). But that's why you're only an engineer and I'm the mathematician.
Shit, you are right. A (careless) error crept into (8) and was carried on to (12). Mea culpa
1 + 1 = 2 can be proven. A fellow student told me that they once did this in an exercise (theoretical physics study). Didn't ask any further questions, but it is definitely not an axiom. Axioms are more basic, such as the definition of natural numbers. Operations defined on this, such as addition (or a certain addition such as 1 + 1 = 2) can then be proven.
Hello, the discussion is a bit fuzzy. When it comes to mathematical objects, mathematicians ask themselves how they can be characterized with as few specifications ("axioms") as possible. This also applies to sets of numbers. The natural numbers can e.g. be defined by the Peano axioms. From this one can then characterize further number sets. The mathematician Cantor formulated this - I believe before Peanos Axoimnen - as follows: God created natural numbers, everything else is the work of man. If you want to know more, continue researching with these bullet points ... Greetings, ..
Hello, I just see that Claus has already expressed himself in the same way, well, then the knowledge deepens through this redundancy. Nevertheless, have fun exploring ...
Supplement to Netbird:> God created the natural numbers, everything> other is the work of man. That's what Kronecker, Cantor's opponent, said. http://de.wikipedia.org/wiki/Leopold_Kronecker
> That's what Kronecker, Cantor's opponent, said.> Http://de.wikipedia.org/wiki/Leopold_Kronecker Aha, and it's correct because it's in Wikipedia? How about looking to more reliable sources when trying to disprove a correct statement?
In our analysis lecture it was said, analogously, "two is just an abbreviation for one plus one, three stands for one plus one plus one, because if you write every natural number as 1 + 1 + 1 + ... + 1 you become yours Life is no longer happy. " So at least at our university it seems widespread that this must be an axiom ... To the roots: In complex mathematics we know the so-called root of unity. That is (at least according to Prof) of the many numbers x that satisfy an equation x ^ n = y, simply the one that has the smallest angle phi in the exponential notation. So in the positive real space (phi == 0) exactly the definition that we know. The proof, in the course of which it is divided by zero, can also be built up more impressively, WIMRE once gave in a special edition of Spectrum of Science. I just don't have it here :(
@Gast: No, it is correct because I read it in a specialist book and it is also in Wikipedia. I only posted the link for people who don't know Kronecker. Now a question: Do you question the statements of people standing in front of you for no reason, or do you only do that in forums?
There are such beautiful, thick books and treatises on this question. What actually is "one"?
According to Prof, it is the one element of multiplication, i.e. f (x) = 1 * x is the identity mapping. But actually a good question, our professor only read from Walter.
> But actually a good question, our professor> always only read from Walter. No, that's not a question, or would you like to philosophize about it? The nice thing about mathematics is that 1000 would-be would-be dudes do not have to give up their mustard for every trivial statement, as in the humanities. Of course, you are free to base your math on other axioms as long as they are consistent, but if you are foreign to such basic ideas as above, nothing useful will come of it. And whether you get your axioms from the Walter, the Egon or whoever, it really doesn't matter. But keep it up, you should always be skeptical after all.
What was meant was the "Analysis" series by Wolfgang Walter. Students of a natural science must have already come across the work. Of course, the math is always the same, and others have philosophized enough. But there are incredibly different formulations that seem practical in different areas, as I was able to experience, for example, in the definition of the scalar product in various lectures. And in quantum mechanics they are all mixed up when discrete and continuous spectra come together ... And with the right formulation, the "proof" for 0 + 1 is much more impressive;)
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