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End of inventing math video
This commit is contained in:
Grant Sanderson
@ -203,7 +203,7 @@ class Mobject(object):
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return (result.real, result.imag, 0)
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return self.apply_function(point_map)
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def highlight(self, color = "red", condition = None):
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def highlight(self, color = "yellow", condition = None):
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"""
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Condition is function which takes in one arguments, (x, y, z).
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"""
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@ -935,15 +935,20 @@ class YouJustInventedSomeMath(Scene):
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mob.shift(UP)
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for mob in text[3:]:
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mob.shift(1.3*DOWN)
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you = draw_you().center().rewire_part_attributes()
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# you = draw_you().center().rewire_part_attributes()
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# smile = PiCreature().mouth.center().shift(you.mouth.get_center())
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you = PiCreature().highlight("grey")
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you.center().rewire_part_attributes()
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self.add(you)
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for mob in text:
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self.add(mob)
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self.dither(0.2)
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self.animate(WaveArm(you))
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self.animate(BlinkPiCreature(you))
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class SeekMoreGeneralTruths(Scene):
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def construct(self):
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summands = [
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@ -987,17 +992,19 @@ class ChopIntervalInProportions(Scene):
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if mode == "p":
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num_terms = 4
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prop = 0.7
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left_terms = map(tex_mobject, ["(1-p)", "p(1-p)"]+[
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"p^%d(1-p)"%(count)
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left_terms = map(tex_mobject, ["(1-p)", ["p","(1-p)"]]+[
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["p^%d"%(count), "(1-p)"]
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for count in range(2, num_terms)
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])
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right_terms = map(tex_mobject, ["p"] + [
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"p^%d"%(count+1)
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["p", "^%d"%(count+1)]
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for count in range(1, num_terms)
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])
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interval = zero_to_one_interval()
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left = INTERVAL_RADIUS*LEFT
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right = INTERVAL_RADIUS*RIGHT
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left_paren = tex_mobject("(")
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right_paren = tex_mobject(")").shift(right + 1.1*UP)
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curr = left.astype("float")
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brace_to_replace = None
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term_to_replace = None
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@ -1023,6 +1030,52 @@ class ChopIntervalInProportions(Scene):
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arrow.points = np.array(list(reversed(arrow.points)))
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additional_anims = [ShowCreation(arrow)]
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if brace_to_replace is not None:
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if mode == "p":
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lt, rt = lt.split(), rt.split()
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if count == 1:
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new_term_to_replace = deepcopy(term_to_replace)
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new_term_to_replace.center().shift(last+UP+0.3*LEFT)
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left_paren.center().shift(last+1.1*UP)
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self.animate(
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FadeIn(lt[1]),
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FadeIn(rt[0]),
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Transform(
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brace_to_replace.repeat(2),
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CompoundMobject(*braces)
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),
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FadeIn(left_paren),
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FadeIn(right_paren),
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Transform(term_to_replace, new_term_to_replace),
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*additional_anims
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)
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self.dither()
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self.animate(
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Transform(
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term_to_replace,
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CompoundMobject(lt[0], rt[1])
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),
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FadeOut(left_paren),
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FadeOut(right_paren)
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)
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self.remove(left_paren, right_paren)
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else:
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self.animate(
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FadeIn(lt[1]),
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FadeIn(rt[0]),
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Transform(
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brace_to_replace.repeat(2),
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CompoundMobject(*braces)
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),
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Transform(
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term_to_replace,
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CompoundMobject(lt[0], rt[1])
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),
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*additional_anims
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)
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self.remove(*lt+rt)
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lt, rt = CompoundMobject(*lt), CompoundMobject(*rt)
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self.add(lt, rt)
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else:
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self.animate(
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Transform(
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brace_to_replace.repeat(2),
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@ -1390,21 +1443,35 @@ class SumPowersOfTwoAnimation(Scene):
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class PretendTheyDoApproachNegativeOne(RearrangeEquation):
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def construct(self):
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you, bubble = draw_you(with_bubble = True)
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start_terms = "1 , 3 , 7 , 15 , 31 , \\cdots\\rightarrow -1".split(" ")
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end_terms = "2 , 4 , 8 , 16 , 32 , \\cdots\\rightarrow 0".split(" ")
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def transform(mob):
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bubble.add_content(mob)
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return mob
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index_map = dict([(a, a) for a in range(len(start_terms))])
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self.add(you, bubble)
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RearrangeEquation.construct(
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self, start_terms, end_terms, index_map,
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size = "\\Huge",
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start_transform = transform,
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end_transform = transform
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num_lines = 6
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da = "\\downarrow"
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columns = [
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tex_mobject("\\\\".join([
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n_func(n)
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for n in range(num_lines)
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]+last_bits), size = "\\Large").to_corner(UP+LEFT)
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for n_func, last_bits in [
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(lambda n : str(2**(n+1)-1), ["\\vdots", da, "-1"]),
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(lambda n : "+1", ["", "", "+1"]),
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(lambda n : "=", ["", "", "="]),
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(lambda n : str(2**(n+1)), ["\\vdots", da, "0"]),
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]
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]
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columns[-1].highlight()
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columns[2].shift(0.2*DOWN)
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shift_val = 3*RIGHT
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for column in columns:
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column.shift(shift_val)
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shift_val = shift_val + (column.get_width()+0.2)*RIGHT
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self.animate(ShimmerIn(columns[0]))
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self.dither()
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self.add(columns[1])
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self.dither()
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self.animate(
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DelayByOrder(Transform(deepcopy(columns[0]), columns[-1])),
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FadeIn(columns[2])
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)
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self.dither()
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class DistanceBetweenRationalNumbers(Scene):
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def construct(self):
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@ -1521,7 +1588,7 @@ class ShiftInvarianceNumberLine(Scene):
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\\begin{flushleft}
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*yeah yeah, I know I'm still drawing them on a line,
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but until a few minutes from now I have no other way
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to draw them"
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to draw them
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\\end{flushright}
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""").scale(0.5).to_corner(DOWN+RIGHT)
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@ -18,19 +18,19 @@ from inventing_math import divergent_sum, draw_you
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class SimpleText(Scene):
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args_list = [
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("Build from the start...",),
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("Build the foundation of what we know",),
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("What would that feel like?",),
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("Arbitrary decisions hinder generality",),
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("Section 1: Discovering and Defining Infinite Sums",),
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("Section 2: Seeking Generality",),
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("Section 3: Redefining Distance",),
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("``Approach''?",),
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("Rigor would dicate you ignore these",),
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("Rigor would dictate you ignore these",),
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("dist($A$, $B$) = dist($A+x$, $B+x$) \\quad for all $x$",),
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("How does a useful distance function differ from a random function?",),
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("Pause now, if you like, and see if you can invent your own distance function from this.",),
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("$p$-adic metrics \\\\ ($p$ is any prime number)",),
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("This does not meant to match the history of discoveries",),
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("This is not meant to match the history of discoveries",),
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]
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@staticmethod
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def args_to_string(text):
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@ -109,7 +109,27 @@ class PowersOfTwoSmall(Scene):
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self.add(you, bubble, bubble.content)
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class FinalSlide(Scene):
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def construct(self):
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self.add(text_mobject("""
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\\begin{flushleft}
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Needless to say, what I said here only scratches the
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surface of the tip of the iceberg of the p-adic metric.
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What is this new form of number I referred to?
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Why were distances in the 2-adic metric all powers of
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$\\frac{1}{2}$ and not some other base?
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Why does it only work for prime numbers? \\\\
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\\quad \\\\
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I highly encourage anyone who has not seen p-adic numbers
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to look them up and learn more, but even more edifying than
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looking them up will be to explore this idea for yourself directly.
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What properties make a distance function useful, and why?
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What do I mean by ``useful''? Useful for what purpose?
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Can you find infinite sums or sequences which feel like
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they should converge in the 2-adic metric, but don't converge
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to a rational number? Go on! Search! Invent!
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\\end{flushleft}
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""", size = "\\small"))
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