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Sep
1
comment Let $V_1,V_2$ be subspaces of $V$. If $\dim(V_1+V_2)=\dim(V_1 \cap V_2) + 1$ then prove that $ V1 \subseteq V2 $ or $V2 \subseteq V1$.
Then what? If $V_1 \subseteq V_2$, this becomes $\dim(V_1)+1=\dim(V_2)$.
Sep
1
comment Let $V_1,V_2$ be subspaces of $V$. If $\dim(V_1+V_2)=\dim(V_1 \cap V_2) + 1$ then prove that $ V1 \subseteq V2 $ or $V2 \subseteq V1$.
The left side is $\dim(V_1+V_2)$, not $\dim(V_1)$.
Sep
1
revised Let $V_1,V_2$ be subspaces of $V$. If $\dim(V_1+V_2)=\dim(V_1 \cap V_2) + 1$ then prove that $ V1 \subseteq V2 $ or $V2 \subseteq V1$.
TeX
Sep
1
comment a bijection is an injective (one-to-one) , surjective (onto) map between sets. if S = (0, 1) and T =R, find a map from S to T which is
$1/|x|$ is not onto.
Aug
15
comment calculate $a/b\ mod\ p$ where p is a prime and a,b can be very large
No, it doesn't. "12/6 mod 3" is 0/0.
Aug
15
comment L'Hôpital or L'Hospital?
This is essentially a copy-paste from Wikipedia.
Aug
6
answered Types of Mathematical “Sameness”
Aug
4
comment Velocity increase while acceleration decrease?
Well, if acceleration is negative at some point and assuming it is continuous, it must increase before it becomes positive.
Aug
4
answered Velocity increase while acceleration decrease?
Aug
3
comment the unit group of an infinite field cannot be cyclic
Ah, it was marked as a duplicate while I fixed this...
Aug
3
revised the unit group of an infinite field cannot be cyclic
added 760 characters in body
Aug
3
comment the unit group of an infinite field cannot be cyclic
Ah, no, in infinite cyclic groups, negative powers are allowed, so $1/a = a^{-1}$...
Aug
3
answered the unit group of an infinite field cannot be cyclic
Aug
3
answered What is the symbol for primes?
Jul
24
comment Group Theory: group under the composition multiplication modulo $p$
In addition, this can be easily generalised to compute inverses in any finite field.
Jul
24
comment Explaining elementary arithmetic in terms of group theory
For example $(\mathbf{R},\times)$ is monoid, but not a group (as is any ring under its multiplicative law).
Jul
24
comment Explaining elementary arithmetic in terms of group theory
You may be looking for monoids, which are essentially to groups what rings are to fields: the requirement for inverses is dropped.
Jul
24
comment Is 1 always an element in multiplicative group?
For reference, this horrible notation $\mathbb{G}_T$ is something many cryptographers have adopted in the context of pairing-based cryptography. In typical scenarios, it is a subgroup of the multiplicative group of a finite field.
Jul
24
comment One divided by infinity is not zero?
Just because something can happen doesn't mean it has non-zero probability. (It's also impossible to generate a uniform probability distribution over the reals, by the way.)
Jul
24
comment Is the subset of squares of a group a subgroup?
The free group on $\{g,h\}$ will do.