Natural Definition and 1000 Threads

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...

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...

At present I am trying to understand the construction of the number systems ... natural, integers, rationals and reals ... What do members of PFs think is the clearest, most detailed, most rigorous and best treatment of number systems in a textbook or in online notes ... ? NOTE: I am currently...

At present I am trying to understand the construction of the number systems ... natural, integers, rationals and reals ... What do members of MHBs think is the clearest, most detailed, most rigorous and best treatment of number systems in a textbook or in online notes ... ? NOTE: I am...

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 1.2.10 ... Theorem 1.2.10 reads as follows: Towards the end (second last line) of the...

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 1.2.10 ... Theorem 1.2.10 reads as follows: Towards the end (second last line) of the...

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 1.2.7 (1) ... Theorem 1.2.7 reads as follows: https://www.physicsforums.com/attachments/6976...

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 1.2.7 (1) ... Theorem 1.2.7 reads as follows: In the above proof of (1) we read the...

Today's Astronomy Picture of the Day discusses a method for determining the distance to a galaxy that I had not seen before. https://apod.nasa.gov/apod/ap170707.html For a far away galaxy, the distance to M106 is well-known in part because it can be directly measured by tracking this galaxy's...

Given any finite set of natural numbers, it seems evident that the odd numbers form a subset of the natural numbers. But what happens "at infinity"? I mean, if we account for all infinitely many natural numbers, there would be also infinitely many odd numbers. In such case, is it still true that...

Science mag news article on a new electrical power plant being set-up by a start-up. It burns natural gas with pure oxygen and runs turbines with CO2. It makes water rather than using it and is in theory close to competitive economically. . Sounds good to me, but I'm no engineer.

Homework Statement https://www.physicsforums.com/attachments/197474 Homework Equations 3. The Attempt at a Solution [/B] ma + kx = 0 I know how to do it if the spring is in the middle of the pulley, not using energy method. by the free body diagram. But I am stuck at this. [Updated: I know...

This work involves partitioning [ \, 0, 1 ] \, into an uncountable number of subsets, using choice to select a single element from each subset, and then defining a bijection from \mathbb{N} onto each subset using that selected element as a reference. The framework allows for proof of two...

Hi, I hoping someone might be kind enough to possibly tell me where I have made an error :) I'm more of a recreational maths person, lol - and I'm trying to make a scheme that 'maps' any decimal number to a natural one. The method I have come up with is a bit odd, I'm hoping it works but still...

as you can see In the image I provided I have derived the equation for i(t) and v(t). On circuit A I use a passive sign convention(current flowing from positive to negative) on the inductor, hence the equation and their corresponding graph. i(t) is decaying exponentially, v(t) is decaying...

as you can see In the image I provided I have derived the equation for i(t) and v(t). On circuit A I use a passive sign convention(current flowing from positive to negative) on the inductor, hence the equation and their corresponding graph. i(t) is decaying exponentially, v(t) is decaying...

Hi guys, does anyone know how to complete proofs of natural deduction for these sequents? ¬ (P ˅ Q), R → P : ¬ R [7] (P & Q) → ¬ R, : R → (P → ¬ Q) [10]the {7} in brackets indicates how many lines each answer should be. I attempted both but my amount of lines were not 7 or 10 Would really...

I am trying to calculate natural frequency for torsional vibration of fixed fixed beam using following formula. =1/2*3.142 sqrt(K*g/mr^2) hz Where K=J*G/L and G=Modulus of rigidity g=acceleration due to gravity=386.4 in/se2 m=mass hanging on the beam at distance 'r' from the longitudenal...

Homework Statement Determine the natural frequency in Hz of the system sketched below given the following values: Mass m=4kg Spring stiffness k=28kN/m Length a=121mm Length b=93mm Homework Equations ω=(k/m)^0.5 The Attempt at a Solution so probably I need to find m should I multiply...

Homework Statement Assuming that an OWC device is floating/moored in monochromatic waves. When there isn't air pressure distribution inside (atmospheric condition) the device behaves as an undambed body (with the oscillating chamber open to the atmosphere). When there is air pressure...

If the sun and cosmic objects are powered by nuclear fusion.. why is there fission in nature via Uranium or Plutonium.. what purpose does it serve for nature since nature doesn't use it. Unless there are natural processes that uses fission or heat from slow fission (maybe heating up the earth)...

A tree seed takes water and minerals(?) from the ground, carbon and oxygen(?) from the air, and heat and light(?) from the sun. When a tree dies and dries up, it can be used as firewood, a source of energy. Is there a way to capture that energy without the seed-tree scenario? i.e., but can we...

I am looking at the definition of the characteristic numbers from the wikipedia https://en.wikipedia.org/wiki/Characteristic_class#Characteristic_numbers "one can pair a product of characteristic classes of total degree n with the fundamental class" I am not sure how is this paring defined here...

Homework Statement A valve is required to regulate the flow of natural gas. Details of the gas are given in table below. It can be assumed that the pipe size and the valve size are the same [i.e. piping geometry does not have to be allowed for]. The chosen valve type is the V250 rotary ball...

Several undergraduate and graduate students and I are building a small engine powered by Compressed Natural Gas (CNG). It is a small and straightforward affair, similar to what is found in small equipment such as chainsaws and lawn mowers. I wanted to experiment with Liquefied Natural Gas (LNG)...

Homework Statement Prove that there doesn't exist natural numbers x and y such that the statement holds true. y^5 + 1 = (x^7-1)/(x-1)The Attempt at a Solution I was able to simplify the term down to y^5 / x = x^5 + (x^5-1)/(x-1) Not sure what to do with it

Hello I have three limits to calculate, based on a given limits. What I know is: \[\lim_{x\rightarrow 0}\frac{ln(1+x)}{x}=1\] And based on this, I need to find (without L'Hopital rule), the following: \[\lim_{x\rightarrow 0}\frac{ln(1-x)}{x}\] \[\lim_{x\rightarrow 0}\frac{ln(1+x^{2})}{x}\]...

Homework Statement find 2017 times A Homework EquationsThe Attempt at a Solution the sum of last members denominator.is 2017 multiplied by 1008 the member before it is 2015 multiplied by 1008 before it 2015 times 1007 2013 times 1007 2013 times 2016 how can i move futher

I came across a guy claiming that the "best approximation" for the natural logarithm of a number is this: ln x=2^n*(x^(2^-n)-1) Oddly enough, it seems to work rather well! I don't really get why it does... I also don't know if it has a limit, I couldn't test it as I don't have access to my...

How can we determine the system properties (natural frequencies & damping ratio ) practically using forced vibration? One way is to measure the phase angle, using the bode plot, the exciting frequency corresponding to 90 (deg) phase shift should be the natural frequency, are there any other...

Homework Statement [/B] Find the natural response V1 is a squarewave Homework Equations KCL, KVL The Attempt at a Solution How would I find the natural response using differential equations? Am I doing it right? by KCL \frac{V_1-V_{in}}{R_1}+\frac{1}{L}\int_{0}^{t}V_1(t)dt +...

Here is a problem I am working on: Using the Rule of Sarrus: $$\begin{vmatrix} x & y & z \\ z & x & y \\ y & z & x \\ \end{vmatrix} =x^3+y^3+z^3-3xyz,$$ find $x, y, z$ such that $x^3+y^3+z^3-3xyz = 315.$ And here is what I have gotten so far: By row and column operations and by factoring out...

What does the N^2 mean in this case? (Image below) Does it mean, for all two pairs of natural numbers, a and b? How would I represent non pair numbers, i.e. how would I write "For integers k,l, and m such that k>1, l>2, m>k+l" all in one line?

Hi, I would like to know if is possible define a set rule explicitly. ex.: Define the set A explicitly where ξ = ℕ and A = {x | x < 3}. The maplesoft said the (N) is a representation of Natural Numbers. f:=proc() local a,b; a:=N; b:= 3; print(a<b); end proc; when I...

I have been in a heated discussion with my acquaintance about natural selection. Anyone who thinks natural selection is a real thing any links would be helpful

I am not sure if this is good, so I would like someone to help me a little and tell me if this is a good proof. I know how to prove that, for example, \sqrt{2} is irrational, so I tried to do something similar with this expression. So, let's assume otherwise, that \sqrt{n+\sqrt{n}} is not...

Homework Statement Prove the following statement: ln|1+\sigma x | = \frac{1}{2} ln|1-x^2| + \frac{\sigma}{2} ln| \frac{ |1+x|}{|1-x|} Homework EquationsThe Attempt at a Solution Starting from right to left would be easier: = \frac{1}{2} ln|(1+x)(1-x)| + \frac{\sigma}{2} ln| 1+x| -...

I have been given an assignment to use a specified distillation column to separate out propene from a gas. The gas consists of propene, propane, ethane and CO2. Separating out the propane has been straight forward, but ethane and especially CO2 are giving me a hard time. To make matters worse, I...

Homework Statement Here is the transfer function of a buck converter I derived: What I need to do next is obtain equations for w0 and ζ. I know how to do this for equations that follow the general form: But in this case I just can't figure out exactly how to do it. How do I find a...

Hello could you help me to solve my task $n \in \Bbb{N}$ Prove that there is n which has more than 2017 divisors d that: $\sqrt{n} \le d < 1,01 * \sqrt{n}$ Thank you

So I'm trying out various practice problems and for some reason I can't get the same answer when it comes to problems involving natural exponentials. Here's the problem A type of lightbulb is labeled as having an average lifetime of 1000 hours. It's reasonable to model the probability of...

I know everything has a natural frequency that is a intrinsic property to the body in question. For example, a string vibrating has the largest amplitudes when it's vibrating near it's natural frequency, and the same thing happens with other things too (like the Tacoma Bridge). Natural...

[Mentor's note: This thread started as a fork of https://www.physicsforums.com/threads/does-the-electron-really-spin-720-degrees.887917.] If you cannot translate the math to language, you are doing something very, very wrong. You are fundamentally at odds with the reality that physics is...

Homework Statement Limx--> ∞ Ln(x^2-1) -Ln(2x^2+3) Homework EquationsThe Attempt at a Solution Ln(x^2-1)/(2x^2+3) Then I divided the top and bottom by x^2 so in the end I got (1/2). Is this right?

Hello everyone. I wanted to prove the following theorem, using the axioms of Peano. Let ##a,b,c \in \mathbb{N}##. If ##ac = bc##, then ##a = b##. I thought, this was a pretty straightforward proof, but I think I might be doing something wrong. Proof: Let ##G := \{c \in \mathbb{N}|## if ##a,b...

MSSM and nMSSM require 5 higgs like bosons in addition to the 126 GEV the SM predicts. thus far LHC has not found any of them. what masses are predicted for Natural SUSY for these additional higgs and how much of a problem is it that the LHC has not found them? if natural SUSY is correct...

I am trying to express some physical constants in natural units of ##c=1## and ##\hbar=1##. Let's start with the electron mass. In SI units, the electron mass is ##0.511 \text{MeV}/c^{2}##. I understand that in natural units, the electron mass is simply ##0.511\ \text{MeV}##. Now, is the...