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Topology

While geometry is primarily concerned with the mathematical properties of spatial objects, topology is concerned with the mathematical properties of those objects under continuous deformations. Please post all questions about topological subjects like homeomorphisms, manifolds, convergence, and connectedness, as well as their broad applications in computing, physics, and graph theory, into this category.

1,087 Questions

How can two nines and two aces give us 10 by using any combination of addition subtraction division or multiplication?

Given these kind of questions, there are often several answers, if we are allowed to freely use the four normal ways of calulating. We will focus on one answer here, however.

We have four cars; two nines and two aces. Remember that the ace card is allowed two values: 1 and 14.

We don't need to complicate matters further, though. We can give one possible answer by simply adding the two aces with the highest value (14) and subtract the two 9's:

(14 + 14)-( 9 + 9) = 10

Written out: 28 - 18 = 10

Why does multiplication by 2 define a bijection from R to R R meaning set of Real numbers but not from Z to Z Z meaning set of integers?

It's not a bijection in Z because it's not surjective. For example, f(x) = 3 has no solution in Z. In other words, you can't double an integer (Z) to get an odd number. It works in R because it's ok to have decimals.

Is Ethernet network usage is based on a bus topology?

Several variations of Ethernet exist. At some moment, a bus topology was quite common, but nowadays, a star or extended star - with a hub or switch at the center of the star - is more common.

Several variations of Ethernet exist. At some moment, a bus topology was quite common, but nowadays, a star or extended star - with a hub or switch at the center of the star - is more common.

Several variations of Ethernet exist. At some moment, a bus topology was quite common, but nowadays, a star or extended star - with a hub or switch at the center of the star - is more common.

Several variations of Ethernet exist. At some moment, a bus topology was quite common, but nowadays, a star or extended star - with a hub or switch at the center of the star - is more common.

How do you make a regular hexagon with equations?

A regular hexagon with one vertex at the origin, and a side along the x-axis and of length s has vertices at:

(0, 0)

(s, 0)

(1.5*s, 0.5*s*√3)

(s, s*√3)

(0, s*√3)

(-0.5*s, s*√3)

Since you now have both endpoints of each line segment, their equations are easy to find.

What is meant by an anholonomic space and an idempotent vector?

An anholonomic space, more commonly referred to as a nonholonomic space, is simply a path-dependent space.

For example, if I went to the kitchen to get a snack, I know that, regardless of what path I take to get back to my room, I will get back to my room. I could have gone outside, on the roof, to a liquor store, or wherever, but the ultimate result from adding up all those paths is that I'll be back in my room. That is because I'm in a holonomic space, or a path-independentspace. Now, if after traveling to all those locations I came back to what I thought should be my room, but instead found myself at, say, the beach, I would be in an anholonomic space, where my destination changes depending on my path taken, ie. my destination is path-dependent.

An idempotent vector doesn't really have any meaning since the concept of idempotence applies to operations. The term idempotence basically just means something that can be applied to something else over and over again without changing it, like adding zero to a real number or multiplying that number by one. That's why a vector, in and of itself, can't be idempotent. However, multiplyinga unit basis vector, ie. one that wouldn't change the magnitude or direction of another vector, to another vector would be an idemtopic operation in a vector space.

How is topology useful today?

Topology is always useful when looking at how a network is physically constructed or wired. This gives the network technician some idea of how the network is put together when diagnosing problems.

How do host on a physical ring topology communicate?

How do hosts on a physical ring topology communication

How many digrees does a scaline triangle have?

The 3 interior angles of a scalene triangle add up to 180 degrees

How is the convergence of a sequence defined?

Let B, D be a metric space, p be any positive number, m be a positive integer, and {sn}, n Є N be a sequence in B. Then sn converges to a point c Є B if given there's an m for every p such that n > m, then sn Є N(c, p), the D-pneighborhood of c. c is said to be the limit of sn and can be written sn --> c.

See related links for more information.

Is there a concept in mathematics that is impossible to prove a thing does not exist?

There is no such concept because it is not true. There are many mathematical proofs based on proving the non-existence of a thing.

The following example should demonstrate.

I want to prove that the biggest number does not exist.

Let us suppose it does exist, and let us call it B (for biggest).

But then consider B + 1.

B + 1 is bigger than B (this can be proved as well).

So B cannot be the biggest number.

That is, there is no such number B. In other words, the biggest number does not exist.

What is a complex combination of pure topologies?

The complex combination of pure topologies is called a Hybrid. Examples of hybrid are star ring network and star bus network.

What are The notion that different measurement bases create a problem of additivity?

Different measurement bases, such as LCM or HC, create the problem of additivity as it is akin to adding height to weight. Also, when using HC, the figure is not particularly relevant due to the issue of changing purchasing power of money.

What is topology?

Topology refers to the physical wiring of a network. There are 4 basic types of topologies:

  1. bus
  2. star
  3. ring
  4. mesh and/or hybrids

Which larger shape would be made if the two sectins are fitted togethr?

Well, honey, if you slap those two sections together, you'd end up with one big ol' shape, now wouldn't you? It's like putting two puzzle pieces together to make a bigger picture. So, to answer your question, the larger shape would be a combination of the two sections fitting snugly side by side.

What devices is most efficient at moving packet between similar network topologies?

A router is the most efficient device at moving packets between similar network topologies. Routers operate at the network layer (Layer 3) of the OSI model and are designed to determine the best path for packets to travel based on destination IP addresses. They use routing tables to make these decisions and can handle different types of network topologies, such as Ethernet, Wi-Fi, and fiber optic networks, making them versatile and efficient for packet forwarding.

How do you draw an isometric projection of a hexagon?

First, you will have to draw circle, and with exact measuring then draw a hexagon. Then make it a cube, and on the top side of this square divide each side by a dot and connect these dots with straight lines. Next, draw a circle in this new, smaller square. On a new paper, copy the previously made small circle. Below the previous one, copy the circle again (so you will have two circles). Make it a cylinder, then copy the cube from the previous draw below this cylinder. Draw the cap for the cylinder on its top, and basically you are done. Additionally, if you have found these instructions a bit confusing, you can search for a video on YouTube on this topic in case you are a visual type.

Which network topology is the best for school network?

It seems like the issue might be related to either the Splunk Universal Forwarder configuration or log file permissions. First, ensure that your inputs.conf and outputs.conf files are correctly set up, with the right log paths and destination indexer details. Check the internal logs, such as splunkd.log, by navigating to /opt/splunkforwarder/var/log/splunk/ instead of /var/log. If no logs are present, verify that the Universal Forwarder has the right permissions to access the log files and is running properly. You can enable debug logging in the log.cfg file for more detailed output and restart the forwarder to apply any changes.

What a star topology uses a to connect all of the nodes?

A star topology uses a central network device, such as a hub or a switch, to connect all nodes in the network. Each node is connected directly to the central device, creating a centralized architecture that simplifies network management and troubleshooting.