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Mathematics

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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-1 votes
1 answer
58 views

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 ...
14 votes
6 answers
1k views

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 ...
2 votes
0 answers
30 views

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 ...
0 votes
1 answer
69 views

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 "...
0 votes
1 answer
78 views

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 ...
3 votes
1 answer
134 views

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.&...
3 votes
0 answers
95 views

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 ...
0 votes
0 answers
37 views

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(...
3 votes
4 answers
506 views

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 ...
0 votes
1 answer
85 views

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 ...
1 vote
3 answers
232 views

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=...
6 votes
3 answers
154 views

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) \...
-2 votes
2 answers
179 views

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 ...
0 votes
1 answer
61 views

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 ...
1 vote
0 answers
97 views

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 ...

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