Anonymous at Tue, 9 Jul 2024 17:07:19 UTC No. 16274394

Look at the graph 1/x.
As x approaches 0 from the left and the right, there is a disconnect or discontinuity on the graph.
Left limit != right limit, so it's undefined.

Anonymous at Tue, 9 Jul 2024 17:09:45 UTC No. 16274404

>>16274394
Grug don't know graph. Grug know common sense.

Anonymous at Tue, 9 Jul 2024 17:22:11 UTC No. 16274436

>>16274404
You're an idiot, so your sense is worthless.
This is why counterintuitive problems exist, because you're too dumb to understand them.

Anonymous at Tue, 9 Jul 2024 17:25:55 UTC No. 16274442

>>16274436
fag

Anonymous at Tue, 9 Jul 2024 17:30:29 UTC No. 16274452

>>16274387
>if 6/2 = 3
>then 2 * 3 = 6
now consider the following:
>if 3/0 = infinity
>then 0 * infinity = 3
>if 4/0 = infinity
>then 0 * infinity = 4
you see the problem? That's why we say anything directly divided by 0 is undefined. It APPROACHES infinity sure, but it's still undefined at 0 itself.

Anonymous at Tue, 9 Jul 2024 17:34:05 UTC No. 16274460

>>16274394
Negative numbers don't exist retard

Anonymous at Tue, 9 Jul 2024 21:07:17 UTC No. 16275008

>>16274394
How do you know there's discontinuity? Maybe you need to make a really big graph and see that the left and right will finally meet somewhere?? Answer it without saying infinity because then your definition of infinity would be circular.

Anonymous at Tue, 9 Jul 2024 21:09:43 UTC No. 16275011

>>16274394
1/0 = infinity
-1/0 = -infinity
That was easy.

Anonymous at Tue, 9 Jul 2024 21:16:47 UTC No. 16275018

>>16275008
It never crosses the y-axis

Anonymous at Tue, 9 Jul 2024 21:18:09 UTC No. 16275024

>>16274387
Infinity is logically contradictory (Finitist gang) so "undefined" is the best answer, since it simply acknowledges there isn't really an actual answer at all. Better than pretending 2 has a square root and inventing a make-believe number for it.

Anonymous at Tue, 9 Jul 2024 21:25:59 UTC No. 16275037

>>16275018
But both sides get closer and closer to y axis so they'd at some point touch y axis

Anonymous at Wed, 10 Jul 2024 01:13:10 UTC No. 16275400

>>16274387
because the moment you allow infinity to be a number you realize their system has infinite amounts of contradictions.

Vote third party at Wed, 10 Jul 2024 01:26:54 UTC No. 16275413

>>16274387
Because you may need and infinitisimal part of something

Anonymous at Wed, 10 Jul 2024 04:26:50 UTC No. 16275577

>>16274394
let the cave boi dream you fiend
https://en.wikipedia.org/wiki/Real_projective_line

Anonymous at Wed, 10 Jul 2024 04:37:35 UTC No. 16275580

>>16275024
W-Wildbergerbros????

Anonymous at Wed, 10 Jul 2024 04:50:17 UTC No. 16275585

>>16274387
>if x/x= 1
>0/x = 0
then what's 1/0 ? you see there are 2 possible answers and that's not how it works , therefore it's undefined

Anonymous at Wed, 10 Jul 2024 16:46:14 UTC No. 16276158

>>16275580
That's who I got the point from my man, he has a spectacular point that it's not that the square root of 2 is irrational... it's that there isn't one.

Anonymous at Wed, 10 Jul 2024 16:49:56 UTC No. 16276162

>>16276158
If you accept rational numbers, then you should accept irrational numbers.
An irrational number is just an infinitely specific rational number.
For example, if you multiply 1.4 by 1.4, you get sorta almost to 2. If you add a few more decimal places, you get closer still. Repeat, and at the limit you'll get exactly 2

Anonymous at Wed, 10 Jul 2024 16:55:41 UTC No. 16276169

>>16276162
>An irrational number is just an infinitely specific rational number.
Rational numbers are already infinitely specific.

Anonymous at Wed, 10 Jul 2024 16:57:20 UTC No. 16276171

>>16276169
sqrt(2) is infinitely specific

Anonymous at Wed, 10 Jul 2024 16:58:03 UTC No. 16276172

>>16276169
Ah, but there are no two finite numbers you can divide into each other that can multiply with itself to be 2

Anonymous at Wed, 10 Jul 2024 18:17:20 UTC No. 16276277

>>16276162
>Repeat, and at the limit you'll get exactly 2
Isn' this kinda a contradiction in terms? I think limits are never actually reached

Anonymous at Wed, 10 Jul 2024 21:42:45 UTC No. 16276591

>>16276171
sqrt(2) doesnt exist and isnt a number.

Anonymous at Wed, 10 Jul 2024 22:36:56 UTC No. 16276646

>>16274387
Correct, but 0 goes into 2 "infinite" times too. As well as any other number you want to name. So whatever you want to call the value this quotient, it can't be considered a number

Anonymous at Wed, 10 Jul 2024 22:46:51 UTC No. 16276658

>>16276646
That's not a response. What excludes 1/0 and 2/0 from having the same result? 1*0 and 2*0 are both the same value, can it also not be considered a number?

Anonymous at Wed, 10 Jul 2024 22:55:51 UTC No. 16276663

>>16276591
it's time to stop posting wildberger

Anonymous at Wed, 10 Jul 2024 22:57:49 UTC No. 16276668

>>16274387
Based Grug

Anonymous at Wed, 10 Jul 2024 23:33:10 UTC No. 16276707

>>16276277
Limits are never reached physically, but mathematically they're well defined and calculable exactly.

Anonymous at Thu, 11 Jul 2024 01:00:09 UTC No. 16276771

>>16276707
Yeah you can calculate the limit but if you're working with a limit then you're saying that what you're doing doesn't actually ever reach there

Anonymous at Thu, 11 Jul 2024 01:10:38 UTC No. 16276777

>>16276771
I'm saying you can reach irrational numbers from rational numbers at a limit by getting more and more accurate
But it's true, you never go from rational fractions to irrational real numbers

Anonymous at Thu, 11 Jul 2024 04:25:13 UTC No. 16276889

>>16276158
My apologies, I like posting screencaps from Wildberger videos when people start assuming stupid things they think he would agree with, like 0.999... ≠ 1
That said, the proof you mention is really just a philosophy on the nature of the contradiction generated from assuming sqrt(2) is a rational number. I think he's put out some pretty good recent videos explaining why he feels that "converges to a transcendental" is affirming the consequent compared to "converges to a rational number".

Anonymous at Thu, 11 Jul 2024 16:31:23 UTC No. 16277479

>>16276889
Do you think, in the actual world of things that genuinely exist and are causally potent, that there could ever be something that truly was the quantity "square root of two"?

Anonymous at Thu, 11 Jul 2024 17:02:39 UTC No. 16277502

>>16277479
I demand that you show me a physical quantity 1 of anything. The number 1 does not exist until you show me exactly 1 of something that satisfies my definition.

Anonymous at Thu, 11 Jul 2024 17:06:59 UTC No. 16277509

>>16277502
Here is a physical quantity of 1 apple. Are you satisfied?

Anonymous at Thu, 11 Jul 2024 17:11:15 UTC No. 16277514

>>16277502
Here is one reply to your post

Anonymous at Thu, 11 Jul 2024 17:16:16 UTC No. 16277520

>>16277509
I don't see 1 of anything. I see a collection of molecules which are only definable as distributions of probability.

>>16277514
I only see a rectangle with words inside it. I don't see one anything.

Anonymous at Thu, 11 Jul 2024 17:34:30 UTC No. 16277549

>>16277520
>a rectangle
a = 1 of something
Your concession is accepted.