![]() ![]() The list of authors can be seen in the page history. The original article was at Increment theorem. Which implies that, or in other words that is infinitely close to, or is the standard part of. In non-standard analysis, a field of mathematics, the increment theorem states the following: Suppose a function y = f( x) is differentiable at x and that Δ x is infinitesimal. Moreover, many calculations depend on being either positive or negative which is impossible if it is made so small that it is zero. The charge of a single electron is definitely not zero but by itself it is insignificant to most calculations. Games that are smaller than any positive number and larger than any negative number are known as small game s. ![]() That is, they are smaller than any positive game and larger than any negative game, but are not larger than zero. In the real world would mean a single electron. Other infinitesimals, like, are confused with zero. To a mathematician might mean zero charge but in the real world there are no charges that small. What makes hyperreals so appealing is that they match how calculus is used in the real world. is called an infinitesimal function as x tends to a. Likewise infinitesimal numbers behave exactly like very small numbers. also implies () for any positive, whose value is not greater than each of the positive numbers. So large that any finite number becomes insignificant in comparison. Infinite numbers, in this system, behave exactly like very large numbers. Hyperreal numbers are an alternate way of conceiving of infinite quantities. ![]()
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