Recent content by strobeda

Thank you, everyone! 1) The surreals contain the reals. 2) A Cauchy sequence comes as close as needed to the epsilon chosen. 3) The construction of reals from Cauchy sequences determines that every rational sequence that converges to x is a representation of x. 4) No construction of R seems to...

Hello, Since nobody ever showed which x is such that x2=2 I confidently fumble on and say: α=sup{x∈R: x2<2} Show ∝∈R; ∝2=2 I also say: ∝≠max Also, I restrict: ∝2not>2 ∝2not<2, ...and then, I wake up and scream: "Can anyone go further?!" Thank you.

Desertation ?

1. Physically, no-motion and no-direction make a vector non-existent. Mathematically, a vector with no magnitude does not perform any function, and we call it the null vector. It is like your car sitting and figuring out which way to go: when you start the engine (preparing the magnitude) you...

I concur (not that it matters to anyone).

Sorry, I overlooked the first question. A null vector has magnitude - it is zero. But it has no direction.

Hello, One opinion: In physics, we refer to Euclidean vector (geometric) as a physical quantity with magnitude and direction. Your car is represented by a bound vector because it has an origin and kept the same direction (eastward) all the time. To decelerate the car means to diminish the...

I suspected that, but I didn't want to go astray trying a wrong tack in case I was just ignorant of the symbol. Thank you very much, pasmith.

Hello, Please, someone, explain what the // in the hint below stands for: "Show that the numbers of the form ±m√2/n for m, n ∈ N are dense." Hint: "To find a number in (x, y), find a rational in (x//√2, y//√2). Conclude from this that the set of all (irrational) numbers of the form ±m√2/n is...

Indeed, it gets ∅ out of the way! Thank you very much, FactChecker!

Hello, I can't wrap my mind around this: inf∅= ∞ sup∅= - ∞ Thank you in advance.

Thank you, WWGD. I will search.

Thank you all! It was the coffee! I didn't see the summation indices (1...n) and (1...m) for the two sums of linear combinations! From the infinite indexed set A, only one finite listing at a time is taken because there is no finite spanning set.

Thank you all! It was the coffee; I didn't see the summation limits! "If A is infinite, we obviously can't use a single finite listing. However, the sum Σ1Σn of two linear combinations of elements of A is clearly a finite sum of scalars times elements of A."

Thank you, Stedwards.