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Mar
14
comment Topological Spaces and Topological Equivalence
By the "power set topology", do you mean the discrete topology?
Mar
14
answered Is there a Turing Machine that can distinguish the Halting problem among others?
Mar
11
comment Negative modulus
@Matt: Whatever is most useful in your context.
Mar
11
answered Negative modulus
Mar
10
comment How many digits does the integer zero have?
So you'd consider an additive system that uses only the symbols "I" for 1 and "X" for 10 (so e.g. XXIII is 23) as base 2, because it uses 2 symbols?
Mar
9
comment How many digits does the integer zero have?
A base $b$ positional system uses digits from $0$ to $b-1$. A base $1$ positional system would therefore only use the digit $0$ — not very useful. Your "base $1$" system rather is the simplest additive number system, that is, it belongs to a wholly different class of number system. It doesn't really make sense to classify it as "base 1".
Mar
8
comment Prove a set is not connected
Yes. Now consider the complement of $A$ and the definition of connectedness.
Mar
8
comment Prove a set is not connected
Hint: If $A$ has no boundary, what does it imply for its openness and closedness?
Mar
7
awarded  Cleanup
Mar
7
revised Subinterval of an interval that has exponential distributed length
rolled back to a previous revision
Mar
7
comment Why is 1 cubic meter 1000 liters?
Because it's convenient?
Mar
7
answered Why is 1 cubic meter 1000 liters?
Mar
7
answered Why is an infinite dimensional space so different than a finite dimensional one?
Mar
4
awarded  Nice Answer
Feb
18
answered Vector space example
Feb
15
awarded  Good Question
Dec
13
comment Why are every structures I study based on Real number?
@TaxxiDriver: Actually I had as possibility in mind the cardinal numbers, for distances between sets. Unlike natural numbers, you cannot extend the cardinal numbers to a field (because of equations like $\aleph_0 + 1 = \aleph_0$).
Dec
13
comment Why are every structures I study based on Real number?
@mbork: Interesting. That one has not even a total order. Is the "addition" here join or meet, or a different operation?
Dec
13
comment Why are every structures I study based on Real number?
@rschwieb: Except that a metric space need not be a vector space.
Dec
13
comment Why are every structures I study based on Real number?
@rschwieb: I wasn't asking about inner products/bilinear forms (there it is obvious that you need a multiplication) but about metrics (a function $d(x,y)$ that is is zero iff $x=y$, is positive otherwise, is symmetric, and fulfils the triangle inequality).