i need help with task 2.23 a.
task “a” asks to show that f is a discontinuous function, but i showed quite the opposite… have i done something wrong?
thanks for help.
#maths
finite jetty
tawdry vaporBOT
i need help with task 2.23 a.
task “a” asks to show that *f* is a discontinuous ...
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finite jetty
@hushed turtle
velvet sapphire
i need help with task 2.23 a.
task “a” asks to show that *f* is a discontinuous ...
alright, this is fairly simple
white dirge
is $0.33=\frac13$?
grizzled forgeBOT
!𒐪 ɹɐupoɯ⇂ㄥ8𝟝 𒐪!
velvet sapphire
we know that 0.11(3) and 1/3 are the points we are evaluating
finite jetty
**!𒐪 ɹɐupoɯ⇂ㄥ8𝟝 𒐪!**
is it not?
white dirge
what is $\frac13$ in decimal form
grizzled forgeBOT
!𒐪 ɹɐupoɯ⇂ㄥ8𝟝 𒐪!
velvet sapphire
bro did NOT have to steal this from me 😭
white dirge
oops
finite jetty
**!𒐪 ɹɐupoɯ⇂ㄥ8𝟝 𒐪!**
0.33?
white dirge
youre missing some of it
finite jetty
what
velvet sapphire
i don’t understand
okay, enter into your calculator 1/3
finite jetty
okay, enter into your calculator 1/3
ok
white dirge
hence it is not equal to 0.33
velvet sapphire
,calc 1/3
grizzled forgeBOT
Result:
0.33333333333333
exactly
finite jetty
hence it is not equal to 0.33
ohhh ok
velvet sapphire
a repeated decimal does not equal to a terminated decimal
finite jetty
while 0.11*3 is exactly 0.33
velvet sapphire
therefore $0.33\neq \frac{1}{3}$
grizzled forgeBOT
;( | 追放された興奮
finite jetty
and thats why it is a discontinuous function
velvet sapphire
👍
finite jetty
**;( \| 追放された興奮**
mhm
dire palmBOT
@finite jetty has given 1 rep to @velvet sapphire
sudden bough
Another way to think about it is 3 * 1/3 = 1, 3 * 0.33 = 0.99.
finite jetty
but where did the 0.99 come from?
sudden bough
...from 3 * 0.33.
finite jetty
yes but why did u do that?
sudden bough
...because we're trying to show 0.33 =/= 1/3.
velvet sapphire
$\sum_{n=1}^{\infty} 3\left(\frac{1}{10}\right)^n$
sudden bough
$\sum_{n=1}^{\infty} 3\left(\frac{1}{10}\right)^n$
n = 1.
grizzled forgeBOT
;( | 追放された興奮
finite jetty
**;( \| 追放された興奮**
wow what does this represent?
sudden bough
wow what does this represent?
...it's 3/10 + 3/100 + 3/1000 + ... = 0.3 + 0.03 + 0.003 + ... = 0.33333....
finite jetty
...because we're trying to show `0.33 =/= 1/3`.
aahh understood
finite jetty
...it's `3/10 + 3/100 + 3/1000 + ... = 0.3 + 0.03 + 0.003 + ... = 0.33333....`
=1/3?
finite jetty
i need help with task 2.23 a.
task “a” asks to show that *f* is a discontinuous ...
so this is where i did wrong?
sudden bough
so this is where i did wrong?
Yes, when you said 1/3 = 0.33.
Here's a trick; a terminating decimal must have a denominator that only has factors of 2 and 5.
hushed turtle