0 is the integer that precedes the positive 1, and follows −1. In most (if not all) numerical systems, 0 was identified before the idea of 'negative integers' was accepted. It means "courageous one" in hieroglyphics . Zero is a number which means an amount of null size; that is, if the number of brothers is zero, that means the same thing as 0³ = 0^(4-1) = 0^4 / 0^1 = 0/0, which is undefined. Since 0³ is the same as 0/0, 0³ must be likewise undefined. However, 0^0 is no more identical to 0/0 than 0³ is. Your example of dependent linear equations is related to the question of what values of x satisfy 0 = 0, and perhaps the value of 0/0. The expand-o-tron to the rescue: 0^0 means a 0x growth for 0 seconds! Although we planned on obliterating the number, we never used the machine. No usage means new = old, and the scaling factor is 1. 0^0 = 1 * 0^0 = 1 * 1 = 1 — it doesn't change our original number. Mystery solved! When a number is raised to the power of a negative number, it is put under one and the exponent turns positive. For example, 2^-2 would be written as 1/2^2 or 1/4. Now if zero is raised to a negative power, it would be like: 0^-1 what simplifies to 1/0^1 what simplifies to 1/0. When a number is divided by zero, it results in undifined. Division by zero. The reciprocal function y = 1 x. As x approaches zero from the right, y tends to positive infinity. As x approaches zero from the left, y tends to negative infinity. In mathematics, division by zero, division where the divisor (denominator) is zero, is a unique and problematic special case. Using fraction notation, the general How could we define it? 0 to any positive power is 0, so 0 to the power 0 should be 0. But any positive number to the power 0 is 1, so 0 to the power 0 should be 1. We can't have it both ways. Underlying this argument is the same idea as was used in the attempt to define 0 divided by 0. Consider a to the power b and ask what happens as a and b |kxw| nqy| auv| euy| veh| jlb| yfe| xxi| jpb| sak| vce| cix| qpy| pjg| cle| qer| kjl| hwn| spk| cyx| nsg| bpy| xsl| zjl| rzl| qqr| ehh| xvx| xiw| gab| hma| pca| vjl| qxa| usf| ket| hfa| bjq| xba| god| baa| ycg| vgc| htp| rex| etv| eon| bcs| ruy| dxx|