Natural Definition and 1000 Threads

Zero is an integer. An integer is defined as all positive and negative whole numbers and zero. Zero is also a whole number, a rational number and a real number, but it is not typically considered a natural number, nor is it an irrational number. Why is 0 not a natural or counting number?

Let Z = set of real numbers Determine if (27/4)/(6.75) is a whole number, natural number, integer, rational or irrational. I will divide as step 1. 27/4 = 6.75 So, 6.75 divided by 6.75 = 1. Step 2, define 1. The number 1 is whole or natural. It is also an integer and definitely a rational...

This is a question arising from the discussion in another thread. It's my understanding that among systems of natural units, the Planck units system sets not only "all three of those to 1", but also does the same with the Coulomb and Boltzmann constants, leaving the elementary charge not...

Hi, I'd like to be clarified regarding the general natural/Neumann boundary condition for a PDE. 1. The natural boundary condition is generally defined as: (1) and can be expressed as, according to this resource: (2) But apparently, according to...

Leavitt's Law allows us to determine how far stars are from us by calculating their variable magnitude of brightness. Please explain how it's possible then for us to see, with the 'natural eye', the distances from one star to another, from one point in the night sky to the opposite, that would...

What is the natural $y$ from $144+{{144}^{49}}+{{144}^{{{49}^{2}}}}+{{144}^{{{49}^{3}}}}+...+{{144}^{{{49}^{2018}}}}=3({{y}^{4038}}-1)$?

Homework Statement The suspension of a modified baby bouncer is modeled by a model spring AP with stiffness k1 and a model damper BP with damping coefficient r. The seat is tethered to the ground, and this tether is modeled by a second model spring PC with stiffness k2. The bouncer is...

Homework Statement Prove that if a set A of natural numbers contains n_0 and contains k+1 whenever it contains k, then A contains all natural numbers ≥ n_0Homework EquationsThe Attempt at a Solution I'm just confused by the question, please don't answer it. Logically it makes sense that if n_0...

I am trying to anallytically determine natural frequencies ƒ of the tympanic membrane. I am using 2D sectorial annulus membrane as a simplified model of tympanic membrane according to following picture The parameters that i want to use are following: THICKNESS = 0,1 mm The natural...

It's a truism that those that are better at surviving/adapting will be better at surviving. How is that in any way enlightening or new? Is there a deeper, more complex aspect to this theory that somehow escaped me? Were there people before this theory believing that those that are worse at...

Let's say you have an impulse of noise, eg. via a guitar string, or a resonant bandpass filter, and it decays naturally. If "1" is the maximum initial amplitude of sound, and "0" is no sound at all, what is the equation for decay of sound over time (x)? Is it: y = 1/c^x Or y = 1/(x+1)^c I...

Homework Statement Calculate the natural circular frequency ωn of the system shown in the figure. The mass and friction of the pulleys are negligible. The diagram is attached. Homework Equations ωn = (k/m)1/2 The Attempt at a Solution I can see the total mass of the system is 3m. So in the...

Hello I am designing a shaft and it will be powered via belt pulley system. The ideal RPM of the shaft is 8000 RPM. How do I calculate the natural frequency of the timing belt to ensure resonance is never met? From what I read online it has to do with belt pretension, but even then I am little...

Homework Statement Find the number of natural numbers n such that (n2-900)/ (n-100) is an integer.Homework EquationsThe Attempt at a Solution I have done the following: (n2-900-9100+9100)/ (n-100) or,{ (n2 - (100)2) + 9100 }/ (n-100) or, (n+100) + (9100)/(n-100) I hope you can understand this...

Homework Statement Prove that ##\forall n \in \mathbb{N}## $$\frac{n}{2} < 1 + \frac{1}{2} + \frac{1}{3} + \ldots + \frac{1}{2^n - 1} \leq n \text{ .}$$ Homework Equations Peano axioms and field axioms for real numbers. The Attempt at a Solution Okay so my first assumption was that this part...

I just asked a similar question, but I got help for that one, and now I am stumped again. I need to find the domain for $$f(x) = ln(x^2-5x)$$ What's confusing me is how to deal with the exponent. I can't think of a way to get around it.

Generally speaking, would it be better to pair a CS/Math minor/minor or minor/major (respectively) with physics or an additional natural science major (e.g., biochem, biophysics, chemistry) with physics? I plan on going to grad school to either pursue a physics Ph.D. or a master's in...

This thread is about the process of theory completion in the practice of theoretical physics, and therefore mostly directed towards practicing theoretical and mathematical physicists, but others can chime in as well. a) What exactly constitutes a natural completion of a physical theory? b) Is...

How is it that when using "natural" units we drop the units themselves. I understand that you can arbitrarily change the magnitude of a parameter by choosing a new unit. For example Oliver R. Smoot is exactly 1 smoot tall. However, in natural units with [c]=[h/(2π)]=1 the "smoot" part is...

In the past, natural selection selected those who are the fittest to live to pass their genes, and eliminated those who are not, but now most people pass their genes, even those who don't have the best genes to live, although now not having the best genes may affect the qualify of a person's...

Hi PF! Given a functional ##J[y]##, if the first variation is $$\delta J[y] = \int_D(ay+y'')y \, dV + \int_{\partial D} (y'+by)y\,dS$$ am I correct to think that when finding stationary points of ##J[y]##, I would solve ##ay+y''=0## on ##D## subject to boundary conditions, which would either...

1. I am using FEA modelling for a vertical heated flat plate and I need to compare theoretical results with the FEA s/w modelling results. I have completed the model in FEA s/w and I'm getting different values for temperatures and because I can't work out theoretical values then I do not know...

Hi, I am trying to gain insight into using stationary vs. rotating coordinate frames for natural frequency calculations. I have seen many FE codes suggest that critical frequencies can be calculated differently in rotating and inertial frames, so i wanted to do a 1D calc to see for myself how...

Hello My name is ron and i am a mechanical engineering in pump factory. In some project i work on, i have fluent that contains sulfur (less then 10 %). my question is how natural rubber react with sulfur? and if its currect to use natural rubber? thanks

Homework Statement [/B] I was reviewing this stuff and although I excelled at it once, I seem to forget some of it. For example, please consider this: Homework Equations R_C=\frac {R_1R_2} {R_1+R_2} + R_3 Here's the correct formula for its error: \Delta R_C=\frac {R_1R_2} {R_1+R_2} \left[...

Homework Statement An appropriate correlation for heat transfer by natural convection from a horizontal pipe to the atmosphere is Nu=0.53Gr^0.25 Pr^0.25 Where, Gr= (αp^2 d^3 (T_1-T_f )g)/μ^2 And Pr⁡〖= (C_p μ)/k〗 Show the above correlation can be simplified to h...

Depleted uranium is often used for applications in which high density is valued, such as counterweights, tank armor, and armor-piercing ammunition. Obviously there are going to be some differences between depleted uranium (defined as having 0.3% or less U-235) and natural uranium (averaging...

Homework Statement My Teacher says that in the Schwarzschild metric he uses natural units, where he writes ##g_{rr}=1-2M/R## He says that for one neutron star ##R=5## corresponds to approx 13 KM. Homework Equations ##1l_p=1,616 \cdot 10^{-35}m## The Attempt at a Solution Unfortunately he does...

The proposition ¬(P→Q) is equivalent to ¬P^Q Does someone maybe have an idea how you can prove (directly) ¬P^Q from ¬(P→Q) by means of natural deduction? I do not manage it. Thanks in advance!

As a physics undergrad, a set of natural units is nothing strange to me, we use them all the time. Having said this, I've never used Planck units. Does any area of research use them on a typical day in the office? There also seems to be this idea that I hear from time to time, perpetuated by...

Homework Statement 1/loga(e) = loge(a) Homework EquationsThe Attempt at a Solution how they are reciprocals of each other ? is their any longer but intuative way to show this result

Now first of all biology is not my strong subject but I am interested in it nevertheless, if my questions come off as arrogant or ignorant then pardon and please explain as I am curious.Last night before going to sleep I suddenly stumbled upon a question, the question goes somewhat like this...

I was watching documentary "David Attenborough's Natural History Museum Alive" where he hides behind the exhibit of some small humanoid skeleton What the heck is this skeleton of? I tried searching it on google but could not find any info.

Hello everyone, Looking for some help on how to go about finding the natural frequency of a block of foam. The foam has a density of 0.37 lbs./ft^3 and is 48"x48"x8" (LxWxD) in size. Weight is approximately 5.4 lbs. I have been digging around the internet for quite some time with no such luck...

Hi, I have a 3mm diameter flexible silicone tube with wall diameter of 0.5mm. If this tube is filled with water at different pressures, how does the internal pressure present itself during modal testing (either shaker or impact testing). The tube lies on rigid table so it is completely...

Homework Statement We have a rod of length L fixed to a rigid support. At the end of the rod there is a mass, m. Assume that the rod has no mass. Find the first natural frequency for the bending, axial and torsion modes. Homework EquationsThe Attempt at a Solution So I'm reviewing some stuff...

Hello guys, I really need help from you about natural deduction. I just can't get to solve theses problems. Can anyone give me the solutions ? I've been trying for hours... Thanks a lot ! Premise 1 : B, Premise 2 : C→(¬B∨A) Premise 3: ¬C→¬(A∨B) Conclusion : A≡C ____ Premise 1: (A∨B)∨C...

Homework Statement To find the natural frequency of a uniform cantilever beam, the area moment of inertia, cross-sectional area and density are not given, everything else is given by the lab, our group got a theoretical natural frequency( it might be angular frequency) of 27.44 Hz from lab's...

Hi Everyone, I have to calculate the coefficients of the massive Higgs Lagrangian in natural units, ħ = c = 1. Do I assume firstly that, in these units the masses of the Higgs, W and Z are the usual, 125.09±0.21, 80.4, 91.2 respectively, and secondly that e has to have the value 2√(απ)...

I am in a physics lab course and we set up the following circuit. Given that we had a 150 milliHenry capacitor and a .5 microfarad capacitor, we calculated the expected resonance frequency using the formula for the natural frequency of an LC circuit: omega = 1/ sqrt(LC). We then measured the...

There are many cyclical phenomena occurring in a nature which have a similar pattern, such as: Farting, Yawning : (Slow buildup of gas over time and then sudden discharge of the gas) earthquake Slow capacitor charging and then sudden discharge Monjolo (Water powered hammer) : Sectarion...

Homework Statement Show that ##(n,n+1) \cap (k,k+1)## is empty, provided that ##n \neq k##. Homework EquationsThe Attempt at a Solution [/B] WLOG, take ##k < n##. Then ##k -n \ge 1## is some natural number. If ##x \in (n,n+1) \cap (k,k+1)##, then ##-(n+1) < -x < -n## and ##k < x < k+1##...

While it's true that it prevents successful penetration by unwanted males, but any unsuccessful fertilization by any males, unwanted or otherwise, results in fewer offsprings. This means lower genetic fitness for convoluted vaginas. EDIT: Not in humans. But in other species in nature such as ducks.

An object only undergoes an oscillation when I act on it. If I push a spring, it will have a certain frequency, and if I push a different way, it will have a different one. What is meant by natural frequency? What is meant by resonance?

Hi everyone!I'm trying to obtain the natural and dual basis of a circular paraboloid parametrized by: $$x = \sqrt U cos(V)$$ $$y = \sqrt U sen(V)$$ $$z = U$$ with the inverse relationship: $$V = \arctan \frac{y}{x}$$ $$U = z$$ The natural basis is: $$e_U = \frac{\partial \overrightarrow{r}}...

hi , hope someone can help as i can't get past a certain step the natural logs is the problem ln⁡((x-1)/(x-3))=2 i can get to this point here -1 = e_x^2-x-3 -1+3=x(ⅇ^2-1) 2 = x(ⅇ^2-1) 2/((ⅇ^2-1) )=x((ⅇ^2-1)/(ⅇ^2-1)) X = 2/(ⅇ^2-1) the solution i got was this x= (2/(ⅇ^2-1)) → 0.3130352855 but the...

Say you have an orange and a banana. You can say that they are two fruits. But this pertains to the categorization of fruit, which could be considered a mental construct of a category. You cannot say that you have two yellow objects, because you really don't. Relative to the category of color...

Find all natural numbers $n$, for which: \[\sqrt{1 \underbrace{4...4}_{n \: times}} \in \Bbb{N}\]

does the natural frequency of a steel rod rigidly fixed will vary when it is assembled with another rod by universal joint?

I am reading Ethan D. Bloch's book: The Real Numbers and Real Analysis ... I am currently focused on Chapter 1: Construction of the Real Numbers ... I need help/clarification with an aspect of Theorem 1.3.7 ... Theorem 1.3.7 and the start of the proof reads as follows: n the above proof we...