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Who first defined truth as adæquatio rei et intellectus? António Manuel Martins claims (@44:41 of his lecture quot;Fonseca on Signs quot;) that the origin of what is now called the correspondence theory of truth, Veritas est adæquatio rei et intellectus
factorial - Why does 0! = 1? - Mathematics Stack Exchange The theorem that $\binom {n} {k} = \frac {n!} {k! (n-k)!}$ already assumes $0!$ is defined to be $1$ Otherwise this would be restricted to $0 <k < n$ A reason that we do define $0!$ to be $1$ is so that we can cover those edge cases with the same formula, instead of having to treat them separately We treat binomial coefficients like $\binom {5} {6}$ separately already; the theorem assumes
Difference between PEMDAS and BODMAS. - Mathematics Stack Exchange Division is the inverse operation of multiplication, and subtraction is the inverse of addition Because of that, multiplication and division are actually one step done together from left to right; the same goes for addition and subtraction Therefore, PEMDAS and BODMAS are the same thing To see why the difference in the order of the letters in PEMDAS and BODMAS doesn't matter, consider the
Why is $\infty\times 0$ indeterminate? - Mathematics Stack Exchange "Infinity times zero" or "zero times infinity" is a "battle of two giants" Zero is so small that it makes everyone vanish, but infinite is so huge that it makes everyone infinite after multiplication In particular, infinity is the same thing as "1 over 0", so "zero times infinity" is the same thing as "zero over zero", which is an indeterminate form Your title says something else than
Prove that $1^3 + 2^3 + . . . + n^3 = (1+ 2 + . . . + n)^2$ HINT: You want that last expression to turn out to be $\big (1+2+\ldots+k+ (k+1)\big)^2$, so you want $ (k+1)^3$ to be equal to the difference $$\big (1+2+\ldots+k+ (k+1)\big)^2- (1+2+\ldots+k)^2\; $$ That’s a difference of two squares, so you can factor it as $$ (k+1)\Big (2 (1+2+\ldots+k)+ (k+1)\Big)\; \tag {1}$$ To show that $ (1)$ is just a fancy way of writing $ (k+1)^3$, you need to
Are we sinners because we sin or do we sin because we are sinners? Thank you for the answer, Geoffrey From what you wrote : 'Are we sinners because we sin?' can be read as 'By reason of the fact that we sin, we are sinners' I think I can understand that But when it's connected with Original Sin, am I correct if I make the bold sentence become like this "By reason of the fact that Adam Eve sin, human (including Adam and Eve) are sinners" ? Please CMIIW