>>7806103 Proof that this number is algebraic and get your cock sucked by the entire mathematics community until the day you die. Watch Terrence Tao get kicked out of UCLA to be replaced by your fat math cock.
Anyways, odds are it is transcendetal. Now way you can trivially construct a number like this.
That is obvious! But your procedure is backwards. The thing to do, is to start with what you know for sure, and then define it, and deduce things from that.
Here's what you know for sure (or some similar/equivalent statement). You want to CONCATENATE (stick symbols next to each other) the prime numbers in their base-10 representations, and then get something back as a real number. So, speaking informally, you could say "let P be the decimal representation of the concatenation of the primes, that is, of infinitely many strings." Then you could write something like
which is just handwaving on my part to suggest what you want in a non-rigorous fashion, but it's clear to any human reading what you/I have in mind. Then you take your newly-defined number, and (just for the sake of having a decimal representation) define its square, which doesn't need anything special (apart from convergence and proving your original number is a real number!), just call the number you want to look at "P^2", say. Thus...
[math] P^2 = 5.55597368... [/math]
So, working in the right direction, first you define one number, then you define the secondary number (in terms of your original number's definition) to get what you want.
Proving that your original number is finite/converges is (partly) elementary. Just observe that it is between 2 and 3. An analysis-minded anon who wanted to quiz you could force you think carefully about successively smaller powers of ten, however, versus your desired concatenation.
Concatenation is very different from addition, anon! Good luck learning math.
>>7806140 Given that there's an infinite set number of prime numbers, then: >2.35711131719... >2 + 0.35711131719... >√4 + * ( * = 0.35711131719... ) If * equals infinity, then: >√4 + 0 (it's either 0.00000...1 or 0.00000.... , finite or infinite. But never a mix of both. So 0.35711131719... can't exist) >result: √4
Not that guy but your retort is foolish, since the ellipsis is simply a mnemonic for any string of digits which "goes on forever". That string may represent either a rational or an irrational number, so if I"m reading your intent accurately (snark/sarcasm, possibly to insinuate assumed irrationality as opposed to simple continuation of a certain pattern), then your intent is wrong.
Well done, also having an improvement on my sketch with sigma notation (as in a literal sum). I assume that that definition relies upon the prime number theorem, just to glance at it (and space digits out appropropriately?!)
But although Champernowne is supposed to be known to be transcendental, I did not see anything in wiki or math world to establish Copeland Erdos as /transcendental/ as such, though it is presumably both irrational and normal.
0/1 = 0.000... 1/9 = 0.111... 10/3 = 3.333... pi = 3.14159... e = 2.718... phi = 1.618...
Pay attention that the first three are rational numbers, while the latter two are transcendental (and therefore by definition, simultaneously irrational) numbers. The final term, on the other hand, is an example of an irrational number which is not a transcendental number, since it is a root of a rational polynomial. Thus, it is said to be /algebraic/.
Now, if you were to retort with something along the lines of "b-but you put a bar over the repeating sequence i-it's not the same I know it!", then this would constitute you missing the point. Which is that ellipses are /a shorthand for some string going on forever/, pattern or no.
Anon, all you're doing is making yourself look stupider by revealing your own wrong assumptions of how math is written, and moving away from the sentiment of your original conceit, which is a few minutes ago, back here >>7806187 . Interestingly, you've confirmed my original suspicion of the unwarranted snark of your earlier comment >>7806140 .
Your central premise, your /point/, hidden behind all your sarcasm and snark, is that ellipses are only used in decimal expansions, or "should" only be used, or are "obviously" only used, when the number in question is irrational. You are wrong on every single one of these points, and I explicitly refuted your central premise here >>7806204 . Because it is obvious to humans who use the glyph, in the sense of natural language, that ellipses denote "continuation", whether patterned or otherwise. And you yourself know this.
But we're past having a conversation, you're just going to double down being wrong, or otherwise do an ad-hom cop out a la "omg don't be so autistic xD", and in so doing, you will have ABANDONED your central point, which will just prove you even more wrong.
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