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Therefore 31 = 7 ⋅ 4 + some number 31 = 7 ⋅ 4 + some number, where your goal is to determine what some number some number is. This same exact process applies for negative numbers. If you want to evaluate −11 (mod 7) − 11 (mod 7), you need the largest multiple of 7 7 that's less than or equal to −11 − 11. This is −14 − 14.
In particular, the logarithm of a negative real number x can then be calculated as log(x) = log(| x | eiπ) = log(| x |) + log(eiπ) = log(| x |) + iπ. However, this explanation is not sufficient and the logarithm as presented is NOT a well-defined function. The angle θ is, well, an angle, and hence only defined up to multiples of 2π: | z ...
And if you take a look at this graph, you will see that. (1 / 2)! = √π 2. This extends beyond negative numbers as well. Indeed, you could even take complex numbers into the scheme: i! = lim n → ∞ n!(n + 1)i (i + 1)…(i + n) Other forms of the extended factorial (Gamma function) may be found on Wikipedia:
1. Change the number into 8 8 bit binary number then take 2 2 's complement; you will get the hexadecimal of negative number. e.g., for −3 − 3 change into binary: 00000011 00000011 take 2 2 's complement: 11111101 = FD 11111101 = F D (hex) Share. Cite.
So −1 ≡ 4 mod 5 − 1 ≡ 4 mod 5, or −1%5 = 4 − 1 % 5 = 4. In general, when you are trying determine a negative number modulo a positive number, you can just keep adding the modulus until you get a non-negative number. Example: To determine −36 mod 7 − 36 mod 7, we do the following computations. −36 + 7 −29 + 7 −22 + 7 −15 ...
ii) positive x negative: add a bunch of negative anti-numbers. The result is a big amount of potential cancelling. Result: negative. iii) negative x positive: take a bunch of positive numbers and take them away. Result: a loss; negative. iv) negative x negative: take a bunch of anti-numbers and take them away.
This advantage holds true for negative numbers with the "round away from zero" rule. -0.15X will always round to -0.2 regardless of X. This works with the "round down" and "round towards zero" rule for negative numbers, but not any other rule. "Round away from zero" is the only rule that has this benefit for both positive and negative numbers.
Notice that in this particular example our base was negative. Since the denominator of the fraction was odd, we were able to solve for a real number. If the denominator were even, though, we would have no real solution, since the even root of a negative number is undefined for real numbers.
I feel like an idiot for asking this but i can't get my formula to work with negative numbers. assume you want to know the percentage of an increase/decrease between numbers. 2.39 1.79 =100-(1.79/2.39*100)=> which is 25.1% decrease but how would i change this formula when there are some negative numbers?
The correct answer is it depends how you define floor and ceil. You could define as shown here the more common way with always rounding downward or upward on the number line. OR. Floor always rounding towards zero. Ceiling always rounding away from zero. E.g floor (x)=-floor (-x) if x<0, floor (x) otherwise.