learning - Where to learn the syntax of mathematics?
14. Learning to write mathematics properly is much like learning to write any language properly, only more so because such a premium is placed on logical organization and clarity. Mathematics, both the part that is written in words and the part that …
soft question - Can you provide me historical examples of pure ...
Jan 17, 2013 · Things that used to be purely mathematical were subsequently used in physics,. Without this pure math, we wouldn't have many achievements in physics, simply because physicists wouldn't have the required theoretical tools to work with. And this means, we wouldn't have engineering achievements that use them. To give some examples:
Mathematics Stack Exchange
1. modified 1 hour ago. 1 vote. 1 answer. 19 views. To prove if there exists a linear transformation that takes a high dimensional complex vector to a scalar injectively. complex-analysis. Matsmir. 3,570.
big list - Conjectures that have been disproved with extremely …
Jul 23, 2010 · Another class of examples arise from diophantine equations with huge minimal solutions. Thus the conjecture that such an equation is unsolvable in integers has only huge counterexamples. Well-known examples arise from Pell equations, e.g. the smallest solution to the classic Archimedes Cattle problem has 206545 decimal digits , namely 77602714 ...
notation - What is "multiplication by juxtaposition"? - Mathematics ...
Apr 16, 2017 · The general consensus among math people is that "multiplication by juxtaposition" (that is, multiplying by just putting things next to each other, rather than using the "×" sign) indicates that the juxtaposed values must be multiplied together before processing other operations. However when talking to certain people they all have said there ...
Is there a mathematical symbol for "For every element"?
It would be too easy to think that this means "for all elements in A" it should read: ∀x; x ∈ A. Which separately says "for all x" and then "x is an element of A". – ashley. Oct 26, 2017 at 18:17. @ashley That's not always right. Some systems of logic admit unrestricted comprehension: "for all x x (in the universe)".
Can you give me some concrete examples of magmas?
May 3, 2014 · 8. One magma that I like is a magma with operation C: {0, 1} → {0, 1} described by this table: It's not commutative, associative, it doesn't have an identity, and has no divisor (if there is no identity, there cannot exist a divisor). Interestingly, for …
What's the correct definition of "conjugate", and do we identify …
Oct 17, 2019 · $\begingroup$ It's not so much that we identify raw values (like $8$ and $2$) as "conjugates", otherwise any two numbers are conjugates.
What do Subscripted numbers in an equation mean?
means that the n -th term of the sequence is obtained by the sum of the 2 immediately previous terms. Usually the subscripts are natural numbers, i.e. a number from {1, 2, 3, …}. That means that the equation above only make sense if n ≥ 3. This means that in order to describe a sequence by the above equation you must specify the values F1 ...
logic - What is the difference between necessary and sufficient ...
It has always been difficult for me to connect the linguistic sense of the terms "necessary" and "sufficient" with mathematics.