Questions tagged [intuition]
Mathematical intuition is the instinctive impression regarding mathematical ideas which originate naturally without regard to formal mathematical proofs. It may or may not stem from a cognitive rational process.
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I have a drawing where I have a sloping line and a point not on that line. How can I draw a line through that point that meets the line. [closed]
I have a drawing that has a sloping line and a point not on that line.
I want to draw a line passing through the given point that intersects the given line in a point outside of the paper.
I believe ...
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What is the correct definition of a limit point in real analysis?
This question relates two (seemingly) conflicting definitions of Limit Points in real analysis.
The definition of limit points and closed sets from my notes are written as:
A much more general ...
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What could have been a good motivation / intuition behind the Dorfman Bracket condition?
I'm a graduate student in Mathematics, currently learning Dirac structures in Differential Geometry. However, I cannot make sense of how the Dorfman bracket condition comes all of a sudden. It ...
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Is there an intuitive way to understand this formula for the magnitude of the projection of one vector onto another? [duplicate]
Let's say it's 200 B.C. and you're tasked with building all of modern math from the ground up. Let's say also that we already intuitively understand the concepts of a "vector", the "...
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How to Read "A Set of Postulates for the Foundation of Logic" by Church
In particular , the first place I feel really lost is with his statement of some basic logical operators as definitions. For example, equality:
$\lambda u \lambda v . P(u, v) . P(v, u)$
Where P is ...
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Why are we satisfied to explain the power of Lebesgue integration just by saying it is ''horizontal, rather than vertical''?
A standard intuition found in textbooks for the power of the Lebesgue integral compared to its Riemann counterpart is that "We integrate by taking horizontal slices, rather than vertical ones.&...
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Higher infinitesimal neighbourhoods as symmetric powers, geometrically [migrated]
Let $k$ be a field of characteristic 0ドル$.
Consider the $k$-algebra $A = k [t_1, \ldots, t_n] / ({t_1}^2, \ldots, {t_n}^2)$.
We can think of $A$ as being the $k$-algebra generated by $n$ linearly ...
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Connections between the surface $x^{3}+y^{3}+z^{3}-3\cdot x\cdot y\cdot z=1$ and the curve $\left(x,y,z\right)=\left(h_{3,n}\left(t\right)\right)$?
What are other relationships between the surface $x^{3}+y^{3}+z^{3}-3\cdot x\cdot y\cdot z=1$ and (the curve defined by) functions $x=h_{3,0}\left(t\right),ドル $y=h_{3,1}\left(t\right),ドル $z=h_{3,2}\left(...
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How many elements are present in the subset of a null set?
Consider :
How many elements are present in the subset of a null set?
This is one of the question that appeared in my math exam.
Definition 1ドル.1$ - Subset:
A set $A$ is a subset of set $B$ if all ...
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A technical question regarding forward passes [closed]
I am a mathematician writing an article on rugby forward passes and am looking for a little help with a definition.
Issue is this:
If I am standing on the 25 metre line and pass the ball laterally ...
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3
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Does $x=y$ imply $ x \leq y$ and $ x \geq y$ (Proof verification). [closed]
I know that $x \leq y$ and $y \leq x$ implies $x=y$ but what about the converse?
This is a proof I have written.
Theorem. If $x=y,ドル then $x \leq y$ and $ y \leq x$.
Proof. We need to prove that if $x=...
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Isomorphism between geometric tangent vectors and derivations
I am trying to understand the proof of the following Theorem:
Let $a \in \mathbb{R}^n$.
a) For each geometric tangent vector $v_a \in \mathbb{R}_a^n,ドル the map $D_{v|a}: C^{\infty}(\mathbb{R}^n) \...
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Prince Rupert's cube - isn't the cube-of-the-same-size problem trivial?
Wikipedia says: "Prince Rupert's cube is named after Prince Rupert of the Rhine, who asked whether a cube could be passed through a hole made in another cube of the same size without splitting ...
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Is it a must for a singular solution to have the dependent variable in it in case of PDE?
Exercise Question given in text book :
For the question (ii) here, from the equation $(2),ドル we could eliminate $a$ and $b$ and say that $xy=1$ is the singular solution. But that was not done here. As ...
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Non Functoriality of Cone Construction & why in $\infty$-Categories this problem disappears
It is well known that in context of derived $(-1)$-categories the cone construction is usually non functorial, ie there is no 1ドル$-functor $\text{Cone}: D(A)^{{\to}} \to D(A)$ from category of arrows ...