![]() So, like ordinary mathematical symbols, hyperreal numbers can be added, subtracted, multiplied, and divided. ![]() So, if I take the number ω and multiply it by ω, I will get ω 2, which you can think of as having two infinite sets of zeroes at the end. What on earth is ω 2? Think of it this way: If I have the number 100 (two zeroes at the end) and I multiply it by 100 (two zeroes at the end), I will get the number 10,000 (four zeroes at the end). We can even square the infinity and have ω 2. ![]() We can multiply infinity by two and have 2 ω. Once you have an infinite unit like ω, you can do a lot with it. If you need a specific number to imagine, think of a 1 with an infinite number of zeroes following it. We don’t have to know which one, we just have to agree that it won’t change. That is, we can say that ω represents some particular infinity. So, if we can’t count to infinity (who has the time?) and there are multiple infinities, which particular one is ω? As it turns out, the particular infinity it refers to doesn’t really matter, provided that we are consistent about it. ![]() So what is ω, exactly? You should think of ω as a kind of unit but, instead of representing a physical quantity (like a foot or a mile or a kilogram), it represents a numerical quantity that is an infinity.Īs we will see, there are many different infinities. Because the hyperreals are new, there is no universal standard for what the notation for infinity should be, so I usually adopt a lowercase Greek omega (ω). Thinking about infinities is somewhat mind-bending, but it turns out that actually manipulating infinities with the hyperreal system is incredibly easy if you are familiar with basic algebra.įor the hyperreals, a new number is introduced to represent infinity. But I have found one particular system to be of more practical use than other systems, which is why I think it is worth discussing. Note that there are actually multiple ways to handle infinitely large numbers. The hyperreal number system extends the reals so as to handle infinity precisely. For instance, the relationship ∞ – ∞ is not zero, but undefined. However, the rules of the real numbers prevent any actual manipulation of these symbols. At most, the real numbers are extended with the positive infinity (∞ or + ∞) or negative infinity (- ∞) symbols to denote numbers too large or too small for the system to handle. The real numbers don’t handle numbers that are infinitely large or their inverses-numbers that are infinitely small. However, some types of numbers are not well represented by the real numbers. For most everyday math, these numbers work really well. Most of us learned the basic number systems in high school-integers (positive and negative whole numbers), fractions (ratios of numbers), real numbers (all those infinitely-continuing decimals), and maybe even complex numbers (with the evil letter “i” lurking around and causing trouble). 10^6 / 80).Share Facebook Twitter LinkedIn Flipboard Print arroba Email If your input always follows the pattern of (only) being in the form of #.#e+006 then you can make this much simpler by taking the value of 'e+') and multiplying it by 12500 (i.e. ![]() Note that this is a simplified example that will not handle negative exponents. If your XSLT processor does not recognize scientific notation, you will have to do the work yourself - for example: ![]()
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