Jack M
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 Feb 8 comment Is it accurate to say that multiplication of two integers yields an integer? @user7530 The important issue that needs to be dealt with here is that the OP thinks they can trust a computer's floating point circuits to tell them about math. This will just be over their head. Feb 8 comment Is it accurate to say that multiplication of two integers yields an integer? I just put $\sqrt 5^2$ into my computer and got $5.000000001$. Computers only do arithmetic approximately. Feb 7 revised Intuitive meaning of the concept “computable” added 204 characters in body Feb 7 answered Intuitive meaning of the concept “computable” Feb 6 comment Squaring both sides when units are different? @TonyK But what does $\sqrt{9 \text{inches}}$ mean? You can't take the square root of an inch any more than you can take the square root of a tomato. The point I was making in my second comment is that your kinematics example has the units outside of the square root, because having them inside is meaningless. Feb 6 comment Squaring both sides when units are different? @TonyK But anyway, with that interpretation the statement in the OP isn't correct - it's not true that $\sqrt 9$ inches equals $\sqrt{0.25}$ yards. Feb 6 comment Squaring both sides when units are different? @TonyK Right, but $x$ here refers to the amount of inches, not the inches themselves, so it's still $\sqrt{2x}\ \text{inches}$, not $\sqrt{2(x\text { inches})}$. Feb 6 comment Squaring both sides when units are different? Are you sure it's not $9^{1/2}\text{inches}=0.25^{1/2}\text{yards}$? Because I don't know what it would mean to take the square root of of an actual physical inch. Feb 5 comment How did the rule of addition come to be and why does it give the correct answer when compared empirically? It seems to me that the way you've phrased the question shows a little confusion. You ask "how" this "came to be", as if it's an arbitrary rule that someone had to invent. 25 + 19 is 44 because if you have 25 coins in one pocket and 19 in the other, then if you tally up the total you find you have 44. What you should be asking is, why is it that "carrying the one" always gives you the correct answer. Feb 2 comment Law of Excluded Middle Controversy At its heart, constructivism is about what it means for a mathematical object to exist. A materialist might already object that mathematical objects don't "exist" - they're just thoughts. At a stretch, you might say they exist because you can imagine them, that is, construct them. And now you come along with an object that not only is purely imaginary, but you can't even describe it or construct it in any way. What sort of "existence" is that? If I understand correctly, excluding the LEM makes non-constructive existence proofs impossible. Someone else will have to explain why. Feb 2 comment Classification of homomorphisms $\mathbb Q \to \mathbb C^\times$ Does the situation change drastically if the injective condition is dropped? Feb 2 asked Classification of homomorphisms $\mathbb Q \to \mathbb C^\times$ Feb 1 asked What is the complexity of the arithmetic operations in base $b$? Feb 1 comment Is this iteration involving primes known? You have the iteration $$x_{n+1} = x_n + p_n + 1$$ Where $(p_n)$ is some sequence of primes (this is what you call $y$ in your question). Therefore $$x_n = x_0 + n + \sum_{k=0}^n p_n$$ You're asking if for any/for all prime $x_0$, we can find a sequence of primes $(p_n)$ such that every $x_n$ is prime. Jan 26 comment Find depth of three node tree Does every node of the tree have three children? Jan 25 comment How to find irrational numbers between rationals. (And is my method correct?) Yes, your method is correct. Basically, given \$a