Logical positivism, also known as logical empiricism, is a philosophical movement that developed in the early 20th century, primarily in the context of the Vienna Circle and the work of philosophers such as Moritz Schlick, Rudolf Carnap, and A.J. Ayer. It sought to synthesize elements of empiricism and formal logic, emphasizing the importance of scientific knowledge and the use of logical analysis in philosophical inquiry.
Logical truth refers to statements or propositions that are true in all possible interpretations or under all conceivable circumstances. In formal terms, a logical truth is typically a statement that can be proven to be true through logical deduction and does not depend on any specific facts or empirical evidence. One classic example of a logical truth is the statement "If it is raining, then it is raining." This statement is true regardless of whether or not it is actually raining because it holds true based solely on its logical structure.
Mathematical axioms are fundamental statements or propositions that are accepted without proof as the starting point for further reasoning and arguments within a mathematical framework. They serve as the foundational building blocks from which theorems and other mathematical truths are derived. Axioms are thought to be self-evident truths, although their acceptance may vary depending on the mathematical system in question.
First import video with:They don't have an
aegisub-3.2 ourbigbook-parent.mkvaegisub executable without the version number. Amazing.If you already have a subtitle file that you want to edit, then just pass it on as well:
aegisub-3.2 ourbigbook-parent.mkv ourbigbook-parent.assEnter: finish editing the current entry and start a new one.
Mathematical logic hierarchies refer to the structured classifications of various logical systems, mathematical theories, and their properties. These hierarchies help to categorize and understand the relationships and complexities between different logical frameworks.
Mathematical logic organizations are professional associations, societies, or groups that focus on the advancement and dissemination of research in mathematical logic and related areas. These organizations foster collaboration among researchers, provide platforms for sharing ideas, and often organize conferences, workshops, and publications in the field of mathematical logic.
In graph theory, an **infinite graph** is a graph that has an infinite number of vertices, edges, or both. Unlike finite graphs, which have a limited number of vertices and edges, infinite graphs can be more complex and often require different techniques for analysis and study. ### Key Characteristics of Infinite Graphs: 1. **Infinite Vertices**: An infinite graph can have an infinite number of vertices.
In this example we will initialize a quantum circuit with a single CNOT gate and see the output values.
By default, Qiskit initializes every qubit to 0 as shown in the qiskit/hello.py. But we can also initialize to arbitrary values as would be done when computing the output for various different inputs.
Output:which we should all be able to understand intuitively given our understanding of the CNOT gate and quantum state vectors.
┌──────────────────────┐
q_0: ┤0 ├──■──
│ Initialize(1,0,0,0) │┌─┴─┐
q_1: ┤1 ├┤ X ├
└──────────────────────┘└───┘
c: 2/═════════════════════════════
init: [1, 0, 0, 0]
probs: [1. 0. 0. 0.]
init: [0, 1, 0, 0]
probs: [0. 0. 0. 1.]
init: [0, 0, 1, 0]
probs: [0. 0. 1. 0.]
init: [0, 0, 0, 1]
probs: [0. 1. 0. 0.]
┌──────────────────────────────────┐
q_0: ┤0 ├──■──
│ Initialize(0.70711,0,0,0.70711) │┌─┴─┐
q_1: ┤1 ├┤ X ├
└──────────────────────────────────┘└───┘
c: 2/═════════════════════════════════════════
init: [0.7071067811865475, 0, 0, 0.7071067811865475]
probs: [0.5 0.5 0. 0. ]quantumcomputing.stackexchange.com/questions/13202/qiskit-initializing-n-qubits-with-binary-values-0s-and-1s describes how to initialize circuits qubits only with binary 0 or 1 to avoid dealing with the exponential number of elements of the quantum state vector.
Structuralism in the philosophy of mathematics is an approach that emphasizes the study of mathematical structures rather than the individual objects that make up those structures. This perspective focuses on the relationships and interconnections among mathematical entities, suggesting that mathematical truths depend not on the objects themselves, but on the structures that relate them. Key aspects of mathematical structuralism include: 1. **Structures over Objects**: Structuralism posits that mathematics is primarily concerned with the relationships and structures that can be formed from mathematical entities.
You get an error like this if you forget to call Related: quantumcomputing.stackexchange.com/questions/34396/aererror-unknown-instruction-c-unitary-while-using-control-unitary-operator/35132#35132
qiskit.transpile():qiskit_aer.aererror.AerError: 'unknown instruction: QFT' Pinned article: ourbigbook/introduction-to-the-ourbigbook-project
Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
Intro to OurBigBook
. Source. We have two killer features:
- topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculusArticles of different users are sorted by upvote within each article page. This feature is a bit like:
- a Wikipedia where each user can have their own version of each article
- a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
Figure 1. Screenshot of the "Derivative" topic page. View it live at: ourbigbook.com/go/topic/derivativeVideo 2. OurBigBook Web topics demo. Source. - local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
- to OurBigBook.com to get awesome multi-user features like topics and likes
- as HTML files to a static website, which you can host yourself for free on many external providers like GitHub Pages, and remain in full control
Figure 2. You can publish local OurBigBook lightweight markup files to either OurBigBook.com or as a static website.
Figure 3. Visual Studio Code extension installation.
Figure 5. . You can also edit articles on the Web editor without installing anything locally. Video 3. Edit locally and publish demo. Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension. 
- Infinitely deep tables of contents:
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact