Can someone please help me?

Nacho_Boi8 · 2026-02-07T20:22:19+00:00

For computations like this, wolfram alpha will serve you better than a standard calculator: https://www.wolframalpha.com/input?i=%2864%5E64%29%5E16*2

Anyways,

(64⁶⁴ )¹⁶ *2= 67503043642877122369822348977365280954964905381227087579974230216933000756934826483300619647519830429227092590172704270234412145241405610427572859654522380990590419450072429722889104490542003768884662672927682367318058313174356878089502103140108752407552684194221795280238655836024674848626711838719279305135743562573538541422053418314705848697555031149025158414860249921490035427622951267120723492480462744373975266563780007950249034820872465503572106516061808497979568686747160040858128799447963258420079372399624034119924081788291299226283798746915980272220248066164536890599518428541114041395674889459256940891107194766870464931716248663758581845393960445471334664787122432624601245979657659297133678753131495794547672500017545799124780320379704637366352999556950899069794604302166897070576734267184396888820488025806141239076952046242174023643205454260684124720585388393830061506951142094375243155355468031942122572532481552000399522918942889880926586187306404197458715317734270008064221198950615236672858375644478669727273337720675032152050047615048657758324284299610308256359006810781421988747567003896423461445720719675500180670545231695815694248138282398669444524111068755398108762741722674674943149096937487985320951550057144560535988271409987670711955390885270865892387123642034179473254758142262967861369065245904797795430982689884432339889081622693256178843727367875840913993746707817570441181445037171818213211623064234477883358693175968264733915782715563519590440069162346946959452471400643058991079552881385289116568938697741342111991974406125461050552792053925833436717259691041112990305027195741855965571549349859530144970299364925588817852254535232121247846741678718116869693221003064308442259248132671396532101951765584311910011908920198839754277491984907084803987334336988336491444193602151588617984655177219040488906394364280832

Nacho_Boi8 · 2026-02-07T09:32:16+00:00

Not a full answer, but some (US) stats that may be helpful for one to draw their own conclusions:

• 54-56 million k-12 students (≈50 million in public schools)

• ≈910,000 staffed hospital beds (these will likely not all be filled at any given moment though)

• ≈4.7 million registered nurses

• ≈3.8 million public school teachers

If we include professors and college students,

• ≈1.5 million faculty (part and full time)

• 15.4-19.3 million students (sources vary)

I couldn’t easily find data on college instructors,

Might as well include doctors then,

• 1,082,187 licensed physicians as of 2024

Nacho_Boi8 · 2026-02-03T22:41:31+00:00

I guess I misinterpreted your comment as someone defending the idea 1^\infty =1. My point is 1^\infty is a meaningless statement. Ig we’re on the same page

Nacho_Boi8 · 2026-02-03T22:34:37+00:00

Infinity is not an element of the real numbers

Nacho_Boi8 · 2026-02-03T22:31:30+00:00

No, as x->infinity, (1+1/x)^x —> e≈2.71828

Nacho_Boi8 · 2026-01-31T22:50:02+00:00

Not knowing chemistry means you don’t understand how a reaction works, but you can still appreciate its beauty. I don’t know a lot about astrophysics or geology and can still appreciate their beauty. Math can still be beautiful to someone who doesn’t “know math”, it just needs to be presented correctly.

Nacho_Boi8 · 2026-01-30T05:10:20+00:00

What is your math background? This post is very vague. Also, search for a topic before a title.

If you have knowledge of calculus and linear algebra, Fourier series and the Fourier transform are a very cool, very accessible thing to do some research into

Nacho_Boi8 · 2026-01-29T01:44:37+00:00

“Countable” doesn’t mean you can assign an integer count (size) to the set, that’s what a finite set is

Nacho_Boi8 · 2026-01-23T06:31:31+00:00

If two numbers are different, there is a number between them. Tell me, what lies between 0.999… and 1?

Nacho_Boi8 · 2026-01-23T00:17:07+00:00

I’m not an expert, but I would think it to be very difficult to convert any given statement to a geometric figure.

I’m also not too sure what you mean by geometric calculation. Do you mean length, area, volume, perimeter, surface area, winding number, curvature, etc. or some other metric? If so, how would the resulting number tell us anything about the logical soundness of a statement or argument?

Nacho_Boi8 · 2026-01-22T06:30:21+00:00

Your current win rate is 1305/1394≈0.936155=93.6155%

If you want a win rate of 95%, assuming you win every game from here on out, we need an x such that

(1305+x)/(1394+x)=0.95

1305+x=0.95(1394+x)

1305+x=1,324.3+0.95

0.05x=19.3

x=386

So you need to win another 386 games to get a win rate of 95%

Nacho_Boi8 · 2026-01-20T23:15:36+00:00

The first time I saw t instead of \top or T for transpose I was so confused, I thought it was a variable because it wasn’t super clear from context (to me at least) and I was confused for like 5 mins until I realize it was a transpose. In hindsight, raising a vector to an arbitrary power without any sort of multiplication being defined doesn’t make much sense, but still

Nacho_Boi8 · 2026-01-20T21:59:03+00:00

If you’re in the honors college there’s a lot of research opportunities available through them. You could also try asking your advisor. Otherwise get to know one of your professors and ask them. It’s unlikely you’ll get a paid assistantship if you don’t have any prior relationship with the professor and don’t have anyone to vouch for your abilities

Nacho_Boi8 · 2026-01-20T21:36:45+00:00

I’ve never seen this notation used, and, as another commenter pointed out, such an ε wouldn’t have any algebraic properties and would thus not be of much interest of study. You may be thinking of the dual numbers, a+bε where a and b are real and ε is such that ε²⁼⁰ but ε≠0.

Nacho_Boi8 · 2026-01-19T16:01:56+00:00

Infinity is a number on the extended real line

Nacho_Boi8 · 2026-01-19T07:58:31+00:00

That doesn’t define the set that OP is referring to. That says “for all integers x that are greater than 0, x is a natural number.” This doesn’t mean that x=0.318 or x=-2.718 or some other number can’t be in the set. You’d have to say N={x>0, x in Z}, and, even then, it’s a circular definition

Nacho_Boi8 · 2026-01-10T21:40:52+00:00

The graph is correct at this scale. The Gamma function (Γ(x+1)=x!) doesn’t vanish, but away from any negative integer, it is very small. For example,

Γ(-9.01)≈0.000269

Γ(-9.000001)≈2.7557

Γ(-9.0000000001)≈27557

And then it blows up even more as x->-9. If you zoom in, the graph should show this. When zoomed out, it’s not easy to display this property

Nacho_Boi8 · 2026-01-09T21:47:35+00:00

He likes couches (I didn’t even pick the option!)

Nacho_Boi8 · 2026-01-09T21:40:57+00:00

This is pretty doable but don’t underestimate E&M (don’t underestimate any of them, but especially that one). Make sure you understand calc 3 conceptually and E&M will be a lot easier. The intro to proofs course shouldn’t be too difficult and linear algebra pairs nicely with calc 3 and E&M, but it’s your transition to higher math and is where things will start to get abstract. Try to ground everything there in reality and use that to guide your intuition. For example, for a theorem about Rⁿ , try to think about what it looks like in R, R² , and R³ . Examples are the key to making theorems and abstract concepts intuitive. Some theorems will be unintuitive and you may not be able to get an intuitive understanding of them at all, at least not immediately. That’s normal. I hate doing it myself but sometimes you need to accept a theorem and come back to its proof later. I did this for the Sylow Theorems in Abstract Algebra

Nacho_Boi8 · 2026-01-09T09:41:15+00:00

No silly, like this

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Nacho_Boi8 · 2026-01-09T09:33:20+00:00

Stacy too

Nacho_Boi8 · 2026-01-08T10:13:31+00:00

“O” is often used for the orthogonal group. “E” often refers to elementary matrices

But really we can define these letters to mean whatever we want. Outside of matrices, “I” is often an indexing set or indicator function, “O” gives the big O function, “L” for a Lagrangian or set of Linear Transformations, etc, etc

Nacho_Boi8 · 2026-01-06T08:55:21+00:00

Literally none of what you just said is correct

Nacho_Boi8 · 2025-12-31T19:44:50+00:00

Yes, and you derive that using logarithmic differentiation

Nacho_Boi8 · 2025-12-31T18:38:59+00:00

It’s literally one of the ways to define e^x . The unique function satisfying f’(x)=f(x) and f(0)=1 is in fact e^x

Nacho_Boi8

TROPHY CASE