Perhaps, this question has been answered already but i am not aware of any existing answer Several years ago when i completed about half a semester of real analysis i, the instructor used introducti. Is there any international icon or symbol for showing contradiction or reaching a contradiction in mathem.
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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. What's so “natural” about the base of natural logarithms Why the number e(=2.71828) was chosen as the natural base for logarithm functions
Mainly i am interested in knowing why is it called natural The number 2 could instead have been chosen as the most natural base. Does anyone know a closed form expression for the taylor series of the function $f (x) = \log (x)$ where $\log (x)$ denotes the natural logarithm function? Thank you for the answer, geoffrey
'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 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. I know that there is a trig identity for $\\cos(a+b)$ and an identity for $\\cos(2a)$, but is there an identity for $\\cos(ab)$
Does anyone have a recommendation for a book to use for the self study of real analysis
