Comments by "L.W. Paradis" (@l.w.paradis2108) on "Mathologer" channel.

  1.  @ejrupp9555  There isn't a largest real number between any two real numbers. Nor a smallest. If a, b are any two real numbers, a < b, there are infinitely many real numbers r such that a < r < b. It's kind of like a one-dimensional fractal, the very same structure repeats on every interval.
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  2.  @ejrupp9555  I think you need to read some math books. The way you formulate these questions is naive. I don't know what you mean by making up a number or getting to a number. Do you think the natural numbers stop somewhere? If it would take too long to write a number (the earth would end long before anyone or any group could write or recite all the zeros in a googleplex), does that number somehow not exist the way 28 exists? If I can write it 10^(10^100) have I just "gotten to it?"
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  3.  @ejrupp9555  I just did, by indicating the sum of an infinite series. Sorry if you don't like them. I'll never understand. No different from using N as a symbol for the natural numbers. That is infinite in precisely the SAME way, perfect one-to-one correspondence. In fact, the elements of N are the exponents of the 1/10. I think you're just goofing around. Divide successive integers by 9 and see whacha get.
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  4.  @ejrupp9555  You know, you're not benign. I'm perfectly serious when I say this is why teachers quit. Anyone who can do this math isn't going to be teaching your kids. OTOH, teaching is a respected profession in many, many places. Basically all, except, well . . . N. B. The dots indicate ellipsis, not an infinite sequence. I know you think this is funny, but I assure you it's not. Not anymore.
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  5.  @ejrupp9555  Say. I have an idea. Why don't you produce an/the "infinitesimal" between 9.99999 . . . and 10.
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  6.  @ejrupp9555  Sorry, this is not coherent. But it does point up the problem with the whole notion of "infinitesimals" -- namely, they blink in and out of existence. Your description of an asymptote is like the difference between open and closed intervals on the real number line. Both [a, b] and [a, b) have the same supremum. The first interval contains its supremum, the second does not. The existence of the second interval does not have any bearing on the possibility of the first. TAKE A TOPOLOGY CLASS.
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  7.  @ejrupp9555  Read a topology book. Infinitesimals do not play any role in standard analysis, none. Absolutely none. Not even a wee bit. And the analogy between asymptotes and open intervals on the real number line was lost on you. The sum of the infinite series 9/10 + 9/100 + ... + 9/10^n + ... really does exist and really is 1. You are thinking of the sequence of partial sums, every one of which is less than one (but not "infinitesimally" less; on the contrary, less to a precise number we can calculate), and you are pretending that that is all that can exist. I'm sorry, but that is wrong. It's like saying open intervals "prove" closed intervals cannot exist. But suit yourself. No one is paying me to post. I'm done now.
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  8.  @ejrupp9555  In fact, I'm giving you too much credit. Most of what you said is not just wrong but muddled. For example, your first statement after the question mark is not coherent.
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  9.  @ejrupp9555  "If 10 were an asymptote" -- except that it isn't. Like, whatever. There are uncountably infinitely many real numbers between 10 and (10 minus epsilon), for any epsilon.
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  10.  @ejrupp9555  Actually, I did a thesis on this for a master's in Ancient Philosophy of Mathematics. In Paris.
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  11.  @ejrupp9555  Don't believe me, LOL!
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  12.  @ejrupp9555  The least upper bound of y is 10. No number less than 10 is in the set of upper bounds of y.
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  13.  @ejrupp9555  Why don't you actually want to know things? The real math is more fun than your ersatz version.
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  14.  @ejrupp9555  I gave you that answer a long time ago. There is no such number. Just like there is no set of all sets. Of course it is simple English. If it were not well defined, we could not say, as we can, definitively, that it does not exist. Look, I understand. YOU can't get to these numbers. I can. I thought mathematics consisted of universal truths. Turns out it's just another part of lived experience. Hope you'll have more luck in the future.
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  15.  @ejrupp9555  Oh, BTW. Blocked and muted.
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  16.  @ejrupp9555  Sure I can. 1/11 = 0.090909 . . . 10/11 = 0.909090 . . . Rational numbers are closed with respect to addition. Hence 9.99999 . . . = (9 + 1/11 + 10/11) = 10.
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  17.  @stanbondarev9256  Then you don't know what transcendental numbers are. Pick up Ivan Niven's book, Numbers: Rational and Irrational (Random House, 1961). Not exactly new stuff.
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  18. @Vorraboms They keep confusing the series with the sequence of its partial sums. The partial sums tend toward the limit. The entire sequence IS equal to its limit. The entire series does not have to be "generated;" it is already there. If it were not, we could not produce its partial sums, of which there are as many as there are positive integers. The 9s in 0.9999 . . . are all already there.
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  19.  @evitthought9641  Prove it with a link. I don't believe he played the same trick.
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  20.  @NotBroihon  And it is not the operation of addition as defined in the algebra of real numbers.
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  21. No. Go back. Please!!!
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  22.  @jongya  EXACTLY. Anything less is elitist. "Cool Smart Guy knows things the rest of us are too lame to grasp." Er, no.
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