Can complex numbers be ordered from 'smallest' to 'largest?
They can be ordered as a set but not as a field.That is, you can define an order on complex numbers quite easily, say by their magnitude: for between any two complex numbers, we can compare magnitudes uniquely, and it is clearly transitive by real number transitivity, this order is transitive.Or, you can use a ‘dictionary ordering’ if you really want to. Imagine ‘looking up’ the first ‘real component’, comparing, and basing order off that, or if they are equal, move down the line, and compare the complex component.But, it doesn’t create an ordering which is consistent with the fact complex numbers add and multiply.That is, an ordered field. This has the added properties that if [math]x>y[/math], [math]x+z>x+y[/math] and if [math]x>0[/math] and [math]y>0[/math], [math]xy>0[/math].Showing the complex numbers can have NO order on them in this respect is easy to show.First, we suppose an ordering can exist: then we have ‘possible options’ like [math]i>0[/math] and [math]i<0[/math], or ‘very wrong’ ones like [math]i=0[/math]. All of these seem weird to even compare: [math]i[/math] is on a whole different axis altogether. Why do we expect it to be comparable to [math]0[/math]? Still, it should be proven.If we have [math]i>0[/math], then by the multiplication property, [math]-1>0[/math] but repeat again multiplication property, this time noting [math]i>0[/math], finding [math]-i>0[/math]. Adding [math]i[/math] to both sides by the former property of ordered fields, get [math]0>i[/math], and so, by transitivity, [math]0>0[/math], a contradiction.Similar holds with [math]i<0[/math]. [math]i=0[/math] is a bit more odd, but if this is the case, should have [math]-1=0[/math], but then that would mean [math]1=0[/math], which contradicts the fact that the complex numbers form a field.You ‘can’ map the complex numbers to a real number line(by using the mapping of 1 euclidean space to 2 euclidean space and use a mapping of two euclidean space to the set of complex numbers). But, this doesn’t create any meaningful order on a field with nice ‘sliding’ properties.
Is -1 larger or smaller than 0.1 (by magnitude)?
If you see a number line,anything that is beyond 0 is smaller than all the numbers which follow 0.Take a look below to understand it in a better way.Every number which lies to the left of the 0 are smaller than 0 and all positive number(even if their magnitude is greater than the positive number)So from above you can see that even 0 is greater than -1 and every other number which possess a negative sign in front of it, is smaller than all the rest of the numbers that lie on the right side of the 0(including 0) .Hence,as you are asking -1 is smaller than 0.5 even if there is a difference in magnitude.Lets understand it with an example, let us suppose that both you and me, have a 100 rupees(its your choice which respective currency you wanna choose).So if I take 10 rupees from you(that is -10) then i will possess 110 rupees(that is +10 is added).Hence you are left with 90 and i m left with 110 rupees from which you can clearly conclude that 110 is greater or in simple language +10 is greater than -10(+10>-10).Hope you understand!!!!KEEP ASKING!!KEEP ANSWERING!!
What is range of the magnitude of floating point numbers?
The range of the magnitude of floating point numbers depends on the representation of the numbers. Several standards exist for representation of floating point numbers, and these standards also dictate the range of magnitude.Custom software can implement whatever representation and range of magnitude is suitable for solving the problem at hand.In general, the range of magnitude of floating point numbers is the interval [0,+1) (the mantissa) to some number of bits of precision, modified by a separately-defined sign and scaling factor, the exponent, a power of two.The common standard for representing a floating-point number in 32 bits is given in IEEE-754. From the wiki article, “the maximum representable IEEE 754 floating-point value is [math](2 − 2^{-23}) × 2^{127} ≈ 3.402823 × 10^{38}[/math]”. You can also find these limits in a C header file called
How do the magnitudes of the H-N-H bond angles vary in these species?
answer a) NH2- < NH3 < NH4+ If an atom has lone pairs and bonded electron pairs, the greater lonepar-lonepair electron-electron repulsions will cause bond angle to decrease between bonded atoms. NH2- - has 2 bond pairs + 2 lone pairs of electrons NH3 - has 3 bond pairs + 1 lone pair NH4+ - has 4 bond pairs bond pair-bond pair electron repulsions < bondpair-lonepair electron repulsions < lonepair-lonepair electron repulsions Greater lonepair -lone pair repulsions among electrons causes the H-N-H bond angle to decrease. This effect is greatest for NH2-, followed by NH3. answer a) NH2- < NH3 < NH4+
What is the definition of magnitude in physics?
Magnitude is a property much like volume or area but is generally concerning a vector quantity.So, I bet you’re asking what is a vector? Well, you have come to the right place: A vector is something that has magnitude and direction.For example, a vector could be displacement. Now if you’re not someone who is experienced with these terms, let me explain.Imagine you’re in a race and you’re at the starting line, if you run 100m your displacement is 100m away from that line. Then if you run 120m back your displacement is -20m (as you’re now behind that line). However, displacement is different to distance as distance is not a vector it is scalar. A scalar quantity has magnitude but not direction.Notice, because in the example you ran backwards, your direction was taken into account when talking about displacement. If we were talking about distance we would say you ran 220m (as you ran 100m + 120m in total, which is the magnitude of the distance travelled) and the direction you were travelling in that time is irrelevant as it is scalar and doesn’t have a direction.Things such as temperature, volume, area all have magnitude (they are either great or small) but don’t have a direction!Hope that helps!
Which car has the largest acceleration?
Use the acceleration equation to work it out. a = (v - u) / t where v = final velocity u = initial velocity t = time taken Put in the numbers and work it out!!!
Which race has the largest population on earth?
By far Mongoloid.Here is a picture of the world grouped into billions. As you can see, South/East Asia has a monopoly over the world. Meanwhile, North and South America, as well as Australia, are all equal to just one billion.Now, this is a mind-blowing image that shows how much of the population lives in Eastern Asia.I don't know about you, but I'm American. I live in a really ethnocentric culture that likes to put a big focus on what we are and ignore most of the rest of the world. Seeing these maps really puts into perspective how wrong that is to do.