Lie Ryan
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 Jul2 comment How would you count a base > 36 system? @user87690: ah, my mistake, yes you're correct, it should actually be base 256. Jul2 comment How would you count a base > 36 system? IPv4 for example is 4 digits of base 255, traditionally denoted as dot separated base 10 numbers (e.g. 255.255.255.255). IPv6 took a similar approach, though the notation is slightly different, with 6 digits of colon separated base 16 numbers (e.g. ff:ee:dd:cc:bb:aa). This is a practical system that can scale to arbitrarily large bases without having to memorize/invent new symbols. Jun23 comment If A = B, then B = A… Not Always True? Definition of “=” In standard math parlance, "=" refers to the equality relation which is an equivalence relation and should always be properly spelled out as "is equal to" or "equals", rather than just "is". Using plain "is" is a poor form because in English "is" can refer to both equality relation or subset relation. Now that that's cleared up, equivalence relation is defined to be a relation which is reflexive. A relation R is said to be reflexive if it holds that if aRb then bRa for all a and b. Sep27 awarded Yearling Aug26 awarded Popular Question Jun23 revised Prove that the additive inverse of an odd integer is an odd integer added 8 characters in body Jun23 comment Prove that the additive inverse of an odd integer is an odd integer I like the simplicity of this approach. Pedantic: you still also need to prove the base case. Jun23 answered Prove that the additive inverse of an odd integer is an odd integer May12 awarded Nice Answer May4 comment A “simple” 3rd grade problem…or is it? You should all know that in these kind of tests, picture is not drawn to scale. That image is actually an image of a board drawn with altered scale to fool students that trued using rulers to get the answer. Apr25 answered How to entertain a crowd with mathematics? Mar8 answered Comparing $2013!$ and $1007^{2013}$ Feb18 comment Where are the values of the sine function coming from? @JackM: I don't think the sin is the only solution that that differential equation. Case in point, $f(x) = 0$, $f'(x) = 0$, $f''(x) = 0$, and $-f''(x) = 0$ is also $f = -f''$. It would not be a good way to define a function. Jan18 answered Can you provide me historical examples of pure mathematics becoming “useful”? Jan7 revised Formalizing the idea of “algorithm” added 72 characters in body Jan7 awarded Revival Jan7 answered Formalizing the idea of “algorithm” Jan7 comment Formalizing the idea of “algorithm” In most formal definitions of algorithm must always have a "terminating condition", i.e. a condition that when reached will mark the end of the algorithm, e.g. when a certain character is found in the sequence (e.g. EOF or your α). A sequence of steps that does not have a terminating condition is usually called computational method/computational process. Dec12 comment Does multiplying polynomials ever decrease the number of terms? If you meant by number of terms as degree, then no, multiplying polynomials would never decrease the degree of the resulting polynomial. If you meant by number of terms as in the number of non-zero coefficients, then others have given examples where it does happen. Nov26 comment Can every proof by contradiction also be shown without contradiction? I usually see the proof stated as the following: Suppose there is only a finite number of primes and ALLPRIME contains all primes in existence. Then ... proof that there exist another number p which is a prime but not in ALLPRIME ... This is a contradiction so there are infinitely many primes. which is a proof by contradiction. I've never seen it presented the way you present it.