What is a chicken? Is it a perceptual construct? You can, of course, define any total ordering you like on it, including ones which are compatible with the total ordering of the real numbers; the problem is that any such ordering will probably not respect algebraic structures within the complex numbers that you might care about. Numbers are concepts. They automatically overestimate the real death numbers, by their own admission. opposite Nice answer! We add 6 before chicken or apple & say 6 chickens or 6 apples. Why were there only 531 electoral votes in the US Presidential Election 2016? Dr. Peet Morris. Incidental fleshy appointments adorning a larger fleshy appendage so named and numbered by the coincidence of thought observing its own fleshy body. Well, colours are real and sizes are real, but what makes a colour 'red'? But so are many other things we take for granted in life. Even if we go on to successfully isolate chickens from all other living birds by definitions, what about the ancestors of chickens who evolved into the modern farm animal? We could claim that it's false, I suppose, but if we are attending a Star Trek convention, that just isn't very polite. Moreover claims like "the concept of number is a useful one" are empirical, yet no evidence is provided to back them up. The person(s) that labeled the numbers could have used green instead of "real" and red instead of "imaginary" and we would have the green number set, the red number set, etc. Numbers are not found in nature. for -ve numbers consider expression integral Perhaps you need something, anything at all to latch onto today, to give you a place to rest your weary mind travelling this vast expanse of possibility. He questioned the "real versus man-made" dichotomy people overuse. The concept of 'chicken' is a tool which we use to understand some of the animals we know about. At some point there weren't chickens, and then there were. Clegg covers a wide variety of subjects to seek out the truth of the matter in an engaging and hugely accessible way. But then one of them comes to us and says: I'm a fan of Star Trek: The Next Generation, and I think your Kirk statement is false. may They are just concepts to help you form words & sentences & thus to communicate with others. I believe that your confusion is due to not realizing that the "labels" used to categorize the various sets of numbers are just that, labels. And so on. The line is a form, which has the same ending as beginning. Numbers help us capture the idea of patterns we find in nature. to found mathematical Asking for help, clarification, or responding to other answers. It's a small-ish bird which doesn't fly very well. What is a toe but a tiny misshapen toe attached to a larger toe? Just like all things, we believe, I believe. (by h.s carslaw), What numbers we find in nature ? For instance, the claim that "Numbers are tools for understanding the world" is not at all obvious, and completely ignores positions like mathematical platonism, or intuitionism, or formalism. Anything else is "crafted" by humans. Following this idea we know for sure that the non-negative integers are real. Similarly do we take the idea there are "numbers" which don't correspond to collections of things as a received idea. or you can create a rule that distributive law holds good if we consider two -ve numbers having a property such (-b*-d) = (+b*d) if 'a' is length > 'b' length and 'c' length > 'd' length then product should be +ve Similarly, we want to include 'six' and probably 'three-halves' and maybe 'negative-two' and 'square-root-of-five' as numbers, but we don't want to include the function f: ℤ→ℤ given by f(x)=3x+2 as a number. (Just because we have different words for things doesn't make them different, but it does mean that we do care about what differences we think they have.) Interesting post (Needs more structure though). I can't be sure, for it may be another that thinks for me, perhaps I just watch them thinking. try putting values in the expression you will find the expression holds good if '? Why did MacOS Classic choose the colon as a path separator? Mathematicians also play with some special numbers that aren't Real Numbers. Thus the line is a 1 dimensional loop, and we observe all numbers as 1 looping itself as 1 set (ie 7 oranges is 1(1+1+1+1+1+1+1) or 1 set of 1's where "orange" is a set and part of the set). Clegg covers a wide variety of subjects to seek out the truth of the … But if you are interested in a world whose rules are unknown to you, there they are helpless. I believe in US. On the other hand there is the No. Lexicographic order on a + bi is one such. from two What would your life be like without them? If knowing something is real is the definition of what is real, then maybe numbers are as real as anything in the universe. The reader goes through the whole history of mathematics and science. So too, our experience with numbers. Why did you think about what a number was and come here to read about it? of Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. No. Thank you @user4894. We do see six eggs or six apples. The colour red is indeed a very useful thing to sense, and to understand, because it is how we perceive some useful physical phenomena. No, I see one image, my 2 eyes function as 1. The thorny issue of "reality" of abstract object (starting from Plato and Aristotle) is that we think that objects are real when we are able to see and touch them, and we cannot see and touch numbers. Is 'equality' ultimately grounded in empirical observation? I think that you are allowing yourself to think of the word "use" differently for 'magic' and for 'numbers', but never mind. The summum bonum is simply that numbers are ideas (mental constructs representing a perception, and in that sense, they do exist platonically). and of the Is time more “real” than math and, if so, why? It depends on what exactly you mean by "real". How do mathematical objects relate to the real world? rests In general, all the arithmetic operations can be performed on these numbers and they can be represented in the number line, also. But fun! be counted in Before reaching this conclusion, Clegg treats readers to an orderly history of math. One might say that all of this we know already, but the author manages to find new interesting angles to approach all the main topics in the book… The description of the emergence of nothing is one of the highlights of the book. Surely 'red' has a fundamental reality beyond our own existence; surely the colour red has an unchanging, even Platonic, nature to it! Again it is interesting to note what we mean by saying 'two apples'. This is why they emphasize on rigor. What do I SEE? Real numbers are used in measurements of continuously varying quantities such as size and time, in contrast to the natural numbers 1, 2, 3, …, arising from counting. Numbers are "real" in the sense that they are a way that man organizes the relative movement between objects he observes in his environment. But that rules out everything but the non-negative integers; and people have historically even looked askance at zero. Even a rich noble would have only had to walk perhaps fifteen minutes and point to an example of a chicken.