🪧 Strange behavior at ♾
We know that rational numbers are closed under addition operation because they form a group. So the addition of 2 rational numbers is rational. As a result, based on associativity property sum of finitely many of rational numbers is also rational. However this is not the case when there are infinite numbers even countably many. For example, sum of reciprocals of factorial of Whole numbers are equal to e, which is irrational(see the figure).
I remember my math professor always say in math when you see infinity stop and think carefully.In many scenarios in mathematics, infinity breaks the ordinary laws and make new ones and behave differently. The beauty here is that inifinty is not just a abstract notation and show itself in real world (e.g. statistical physics and complex systems) and emerge interesting phenomenon. Since childhood, I've been in a quest for deeper undersranding of infinity concept. Therefore, I decided to take a look at Georg Cantor's great work to gain a better comprehention. I'll write about it briefly.
I'll eagerly looking forward to hear your comment.
#Note #Math
@SingularThinker
We know that rational numbers are closed under addition operation because they form a group. So the addition of 2 rational numbers is rational. As a result, based on associativity property sum of finitely many of rational numbers is also rational. However this is not the case when there are infinite numbers even countably many. For example, sum of reciprocals of factorial of Whole numbers are equal to e, which is irrational(see the figure).
I remember my math professor always say in math when you see infinity stop and think carefully.In many scenarios in mathematics, infinity breaks the ordinary laws and make new ones and behave differently. The beauty here is that inifinty is not just a abstract notation and show itself in real world (e.g. statistical physics and complex systems) and emerge interesting phenomenon. Since childhood, I've been in a quest for deeper undersranding of infinity concept. Therefore, I decided to take a look at Georg Cantor's great work to gain a better comprehention. I'll write about it briefly.
I'll eagerly looking forward to hear your comment.
#Note #Math
@SingularThinker
👍3
Three logicians walk into a bar.
The bartender asks: 'Does everyone want a drink?'
The first logician says: 'I don't know.'
The second logician says: 'I don't know.'
The third logician says: 'Yes.'
Got it?
#Math
@SingularThinker
The bartender asks: 'Does everyone want a drink?'
The first logician says: 'I don't know.'
The second logician says: 'I don't know.'
The third logician says: 'Yes.'
Got it?
#Math
@SingularThinker
Singular Thinker
خب بلاخره به قولی که به خودم داده بودم عمل کردم و وقت به اشتراک گذاشتن این پست رسید. شادی تحویلدارزاده انسان بسیار جالبیه، ریاضیدان، دوستدار علم و داستانگویی صادق و شیرین سخن. از آن دسته آدمها که روایتشان چون که مملو از صداقت است احساسات شما را درگیر…
خب در ادامهی این پروژه رفتم سراغ قسمت تینا ترکمن که به تازگی از هاروارد فارغ التحصیل شده و قراره پست داکش رو شروع کنه. تینا خیلی شخصیت جالبی داره و خیلی گیرا و صادقانه صحبت میکنه نمیدونم چرا حس کردم مثلا به صحبتهای دوستم دارم گوش میدم.
از ماجراهای زندگیش تا امروزش میگه از لحظات تلخ و شیرین، دیدش به زندگی و درس خوندن و PhD و از تلخیهایی که تو این مسیر به عنوان یک دختر تو ایران داشته هم اشاره میکنه. استاد راهنمایی که تو هاروارد داشته هم واقعا آدم جالبی بوده. خلاصه من که حال کردم دوست داشتید شما هم گوش کنید.
🔗 لینک مصاحبه
#آدمها_و_ریاضیات
#podcast #math
@SingularThinker
از ماجراهای زندگیش تا امروزش میگه از لحظات تلخ و شیرین، دیدش به زندگی و درس خوندن و PhD و از تلخیهایی که تو این مسیر به عنوان یک دختر تو ایران داشته هم اشاره میکنه. استاد راهنمایی که تو هاروارد داشته هم واقعا آدم جالبی بوده. خلاصه من که حال کردم دوست داشتید شما هم گوش کنید.
🔗 لینک مصاحبه
#آدمها_و_ریاضیات
#podcast #math
@SingularThinker
YouTube
TINA TORKAMAN
آدمها و ریاضیات؛ گپ و گفتی کنجکاوانه، صادقانه و بیپرده با آدم هایی که زندگی حرفه ای آنها به ریاضیات گره خورده است؛ فصل ۴، شماره ۱. تینا ترکمان
0:00:24 نقاش که نشدم
0:01:59 و خواهری که در این نزدیکی است
0:05:02 آزادی درس نخواندن
0:08:20 حس خوب خوشبختی…
0:00:24 نقاش که نشدم
0:01:59 و خواهری که در این نزدیکی است
0:05:02 آزادی درس نخواندن
0:08:20 حس خوب خوشبختی…
👍5❤2
#linear_algebra
Given subspaces V_1, V_2, …, V_n, (n>2)we know that the intersection of all pairs of these subspaces consists of only the zero element (V_i Ո V_j = {0}). Is the sum of these subspaces a direct sum?
Given subspaces V_1, V_2, …, V_n, (n>2)we know that the intersection of all pairs of these subspaces consists of only the zero element (V_i Ո V_j = {0}). Is the sum of these subspaces a direct sum?
Anonymous Poll
47%
Yes.
53%
No.