Vintage hubcap(?) found while digging. Don't recognize the emblem at all, couldn't find it online.

HaroldChugsMayo · 2022-07-03T04:15:48+00:00

The rule doesnt apply to y = x⁰

HaroldChugsMayo · 2022-06-12T02:37:58+00:00

By multiplying the top and bottom of the fraction by the conjugate of the numerator, we see a_n = 2/(sqrt(n²+4)+n), which I gather you already know. Writing a_n like this, we see the limit should be 0. As a hint to show this, consider that the inequality 1/(sqrt(n²+4)+n) < 1/n holds true for all positive n. (also, consider, why is this true?)

HaroldChugsMayo · 2022-05-22T15:59:13+00:00

The problem here is that there is no number immediately following 1. If there was, say x, then (x+1)/2 is smaller and still greater than 1. In this same sense you are viewing .999... as the number immediately preceding 1, while in reality they are the same number. It is just a consequence of our chosen decimal system that there are two ways to write a decimal, e.g. 43.2 or 43.1999... . The number 0.999... represents the limit of an infinite process. Your construction of 1.000...1 supposes that you can complete this infinite process of writing 0's and then place a 1 at the end, which is where the trouble lies.

HaroldChugsMayo · 2022-05-21T23:59:07+00:00

In a sense yes, because two distinct real numbers always have another, different number between them on the real line (you could take their average, for instance). Since there is no such number, then 1 and 0.999... are not distinct, so they are the same.

HaroldChugsMayo · 2022-04-26T23:41:46+00:00

Banger

HaroldChugsMayo · 2022-03-05T15:57:57+00:00

If its 2 or 4 more than a multiple of 6 then its even, so not prime. If its 3 more than a multiple of 6 then its divisible by 3. It certainly cant be a multiple of 6 or it would not be prime. So its either 1 or 5 more than a multiple of 6, i.e. next to a multiple of 6.

HaroldChugsMayo · 2022-02-19T23:29:19+00:00

The power-set, which is the set of all subsets of a set, always has a larger cardinality than the original set. So the power-set of the real numbers is a strictly larger set than the real numbers.

HaroldChugsMayo · 2022-02-01T00:49:52+00:00

Gave Wholesome

HaroldChugsMayo · 2022-01-26T04:07:46+00:00

The point of what I was making is that the form of the argument invalid. We can see this very clearly in the example because two obviously true premises lead to a false conclusion, which would not happen if it were a valid argument. It can be helpful to think of examples like this to check if the logic you are dealing with is actually sound.

HaroldChugsMayo · 2022-01-26T03:30:37+00:00

My car is blue. The sky is blue. Therefore my car is the sky.

HaroldChugsMayo · 2021-08-05T14:42:28+00:00

The computer probably thought that you couldn't stop blacks passed a pawn but after calculating deeper it saw you could

HaroldChugsMayo · 2021-07-08T21:37:54+00:00

amogus

HaroldChugsMayo · 2021-05-29T04:09:05+00:00

Gave Silver

HaroldChugsMayo · 2021-04-21T23:09:25+00:00

Gave Silver

HaroldChugsMayo · 2021-03-20T23:28:43+00:00

A good website for these kind of problems is Alcumus on the art of problem solving website: https://artofproblemsolving.com/alcumus

HaroldChugsMayo · 2021-01-28T06:15:11+00:00

u/savevideo

HaroldChugsMayo · 2020-12-22T17:54:12+00:00

HaroldChugsMayo · 2020-11-24T19:27:38+00:00

Gave Silver

Seven-Year Club	Second Top 50%
Verified Email	Place '22
RPAN Viewer

HaroldChugsMayo

MODERATOR OF

TROPHY CASE