@@JTtheking134 what? Everything I know I learnt on UA-cam or the internet for free. My high school didnt gaf and college only ever cared about my tuition fees being paid.
@@idkjustleavemebeplease sorry to hear that, my comment was based on an assumtion and im sorry for that. I havent begun highschool yet. (I have a highschool maths book tho but man youre right this is so slow)
@@JTtheking134 oof, that imbetween was the worst for me. It always seemed like they glossed over important stuff and drew out simple bs for so long. Best of luck in your studies. Stick with youtube, you'll learn a ton. You'll also learn about why things work the way they work which is arguably better than anything school ever taught me.
@@idkjustleavemebeplease Yeah! This! Intuitive proofs are so important and understanding why something works is very important for a higher level of understanding yet school somehow missed that its important.
Because particular odd and even integers are being taken. It is like saying: if n is even, then there exists an integer k such that n=2k, and vice versa.
The English language is pretty confusing. The statement "for some integer k" really just means that at any particular value of k, the given statment is true. K could be any integer which means what you said.
i wonder how knowing things like this would change life .. (had to drop out of school at age 14.. no clue what maths is all about - other then simple 1+1=2 and some light fractions im pretty much lost .. but i wonder if i had been able to go to school and actually study and know things lke this if it would have changed my life, .. okay tis sounds crazy .. but i think all knowledge we have shapes who/how we are, so it changes our perspectives on things .. okay im babbling now .. time for a movie and pringles! youtube send me on a rabbithole w vids that make me go "hmm " (ps u got a nice voice sir)
@@rishikkeshari6306 I got stuck in life at age 14 ... i live from a disability check because i am unable to work idk how to even do life .. so yeah .. no job nothing to be proud of other than i have 0 dept eventho i live at the lowest income in my country
I have never taken a math foundations class so this may be completely wrong. But here is what I got and I'm curious to see how close it was (haven't watched the video yet). n odd m=n-1 m even n=m+1 substitute for n: 3n + 7 = 3(m+1) + 7 distribute: =3m + 3 + 7 add 3 and 7: =3m + 10 take out a 2: =2(1.5m + 5).....(1) 1.5m = 1m + 0.5m but m is even, so by definition, 0.5m is an integer p --> 1.5m = 1m + 0.5m = m + p (1) becomes: 2(m+p+5) m, p, and 5 are all integers, so m+p+5 is also an integer q so we end up with: 2*q where q is an integer 2*integer = even number QED? Criticize please
Good evening, I'm just going to point out what I see is wrong. First of all, anyone is welcome to correct me, I'm just a first year mathematics student at college, so I may be missing something but here's my take. We are working with integers, so we can not go outside the given set of numbers, because in this problem or, in general, talking about even and odd numbers we refer to numbers with no decimals, as far as I'm concerned and, a decimal representation of a number is nothing but a rational number or an irrational number, none of which are in Z, the set of integers, (Z:={0,1,-1,2,-2,...}). Now that we are familiar with the set we are working on, we need to prove that given any n in Z such that n is odd, then 3n+7 is even. First of all, what does that mean? Well, if an even number is a number such that when we divide by 2 there is no remainder, i.e., is 0, then, an odd number is a number such that when we divide by two you have 1 as remainder (the remainder is a positive integer (Z^+=:{0,1,2,3,...}) such that is grater or equal to 0 and strictly less than the divident in order to have de division properly defined so, in our case, that remainder can only be 1 because we have reasoned that it can't be 0 or 2, because n is not even), althoug I would say that it's easier to understand (it can be proven (in fact, I let it to you as an exercise)) that if n is odd then n+1 is even and viceversa, so, given n odd, that means that it can be written as a multiple of 2 plus 1, i.e., n=2m+1 for some m in Z. Now, following what you did, we substitute n in the given equation and we'll see that a factor of 2 can be extracted as a common factor and what we are left with is 2 times something that is in Z, hence, the given expression is, in fact an even number. -How I would write the proof: Let n be an odd integer, then, we want to show that 3n+7 is even. If n in Z is odd then we can rewritte n as follows: n=2m+1 for all m in Z. Now, we substitute our parametrized n in the given expression: 3n+7= =3(2m+1)+7= =6m+3+7= =6m+10= =2(3m+5) taking a common factor of 2 out. We notice then that we have ended up with 2α, where α=3m+5 which is a number in Z. Hence, 3n+7 is even for all n in Z such that n is odd. Q.E.D If you have any doubt I'm more than happy to respond!!
Humanity has ten numbers (0, 1, 2, 3,...9) Newton: "0 is contingent" 🚫 and "1-9 are necessary" 🚫 (this is the basis of Newton Calculus/Physics/Logic). Leibniz: "0 is necessary" ✅ and "1-9 are contingent" ✅ (this is the basis of Leibniz Calculus/Physics/Logic). Is zero the most important number? Zero is the most important number in mathematics. Zero functions as a placeholder. Imagine a number, e.g., 5 and put as many zeroes behind it as you can think of. Zero drastically changes the value of the number from a mere 5 to 50, 500, 5000, 50000 and beyond. Which is the greatest whole number? There is no 'largest' whole number. Every whole number has an immediate predecessor, except 0. A decimal number or a fraction that falls between two whole numbers is not a whole number. Why is it impossible to divide by zero? The short answer is that 0 has no multiplicative inverse, and any attempt to define a real number as the multiplicative inverse of 0 would result in the contradiction 0 = 1. Is 0 a rational number? Yes, 0 is a rational number. Since we know, a rational number can be expressed as p/q, where p and q are integers and q is not equal to zero. Thus, we can express 0 as p/q, where p is equal to zero and q is an integer. Is 0 A whole number? The whole numbers are the numbers 0, 1, 2, 3, 4, and so on (the natural numbers and zero). Negative numbers are not considered "whole numbers." All natural numbers are whole numbers, but not all whole numbers are natural numbers since zero is a whole number but not a natural number. Why is 0 a good number? Zero helps us understand that we can use math to think about things that have no counterpart in a physical lived experience; imaginary numbers don't exist but are crucial to understanding electrical systems. Zero also helps us understand its antithesis, infinity, in all of its extreme weirdness. 🔘 ♾ ☯️ Who is pushing Newtonian Calculus/Physics/Logic? The man was a moron (and a fraud who used political power to "win"). Our fundamentals are off because our fundamentals are directly "idiot" Issac Newton's fundamentals. Our universe doesn't match Newton's illogical nonsense. Theory of Everything is Cosmogony, Cosmology and Quantum and Newton is buttcheeks at all three. Nothing lines up. Hard swap to Gottfried Leibniz. Also, Aether > Gravity. (Miller crushed Gravity so hard they had to wait more than a decade after his death to start weasling Newtonian logic a "win" again by burying Miller’s Aether theory). Also, Tesla > Edison. (3D height, 6D depth, 9D absorption i.e. contingent universe) fundamental = rock particular = sand
The whole magic of the calculus thing is that their two processes lead them to exactly the same place. They can't be one right and one wrong, because at the end of the day, they have the same conclusions.
I don't know what level this is intended for, but might as well mention, you have made implicit use of the distributive property, and more deviously, that arbitrary sums and products of integers remain integers (given integer k, 3k+5 is an integer). But again, I don't have the full context, and maybe you have already proven some things about the integers as a field, but even if you did, you certainly didn't invoke it here in this short. Usually an important point of these low-level proofs is to really scrape the bottom, to see, like, "oh wow I actually can't get there without assuming I'm in a field, I wonder if this only holds in fields", etc. Just assuming intuitive properties of arithmetic is like, if we were allowed to do this, I would assume the whole statement to be proven :P
❤Only for fans over 18 year⤵️ Alles sehr schön. Aber zuerst zusammen die Nummern 10 und 1. Eine Babymomm.beauty Brünette und eine andere Blondine. Es wäre unfair, wennu ich 4 wählen würde
if n is odd, 3n will always be odd (proof: basic intuition ie. 2n+n = even + odd = odd) => 3n+7 = odd + odd = even always. it's pretty fucking basic why even make a video about it lmao
I genuinely feel like if I had a hand book that explained notation and the proper rules, I'd be able to fully calculate anything.
Thats school for you. Just remember that every1 dont have it that easy, and school is on a budget, so this is very slow unfortunately
@@JTtheking134 what? Everything I know I learnt on UA-cam or the internet for free. My high school didnt gaf and college only ever cared about my tuition fees being paid.
@@idkjustleavemebeplease sorry to hear that, my comment was based on an assumtion and im sorry for that. I havent begun highschool yet. (I have a highschool maths book tho but man youre right this is so slow)
@@JTtheking134 oof, that imbetween was the worst for me. It always seemed like they glossed over important stuff and drew out simple bs for so long. Best of luck in your studies. Stick with youtube, you'll learn a ton. You'll also learn about why things work the way they work which is arguably better than anything school ever taught me.
@@idkjustleavemebeplease Yeah! This! Intuitive proofs are so important and understanding why something works is very important for a higher level of understanding yet school somehow missed that its important.
when you add odd number, it flips result:
n is odd
n+n is even
n+n+n is odd
n+n+n+7 is even
This proof is easy. That's the exact method I did in my head.
When you write the recall statements why do say some integers instead of all integers?
Because particular odd and even integers are being taken. It is like saying: if n is even, then there exists an integer k such that n=2k, and vice versa.
The English language is pretty confusing. The statement "for some integer k" really just means that at any particular value of k, the given statment is true. K could be any integer which means what you said.
For each integer x there is some integer k that satisfies the condition
i wonder how knowing things like this would change life ..
(had to drop out of school at age 14.. no clue what maths is all about - other then simple 1+1=2 and some light fractions im pretty much lost .. but i wonder if i had been able to go to school and actually study and know things lke this if it would have changed my life, .. okay tis sounds crazy .. but i think all knowledge we have shapes who/how we are, so it changes our perspectives on things .. okay im babbling now .. time for a movie and pringles!
youtube send me on a rabbithole w vids that make me go "hmm "
(ps u got a nice voice sir)
What do you do for a living?
@@rishikkeshari6306 I got stuck in life at age 14 ... i live from a disability check because i am unable to work
idk how to even do life .. so yeah .. no job
nothing to be proud of other than i have 0 dept eventho i live at the lowest income in my country
I have never taken a math foundations class so this may be completely wrong. But here is what I got and I'm curious to see how close it was (haven't watched the video yet).
n odd
m=n-1
m even
n=m+1
substitute for n:
3n + 7 = 3(m+1) + 7
distribute:
=3m + 3 + 7
add 3 and 7:
=3m + 10
take out a 2:
=2(1.5m + 5).....(1)
1.5m = 1m + 0.5m
but m is even, so by definition, 0.5m is an integer p
--> 1.5m = 1m + 0.5m = m + p
(1) becomes:
2(m+p+5)
m, p, and 5 are all integers, so m+p+5 is also an integer q
so we end up with:
2*q where q is an integer
2*integer = even number
QED?
Criticize please
Good evening, I'm just going to point out what I see is wrong. First of all, anyone is welcome to correct me, I'm just a first year mathematics student at college, so I may be missing something but here's my take.
We are working with integers, so we can not go outside the given set of numbers, because in this problem or, in general, talking about even and odd numbers we refer to numbers with no decimals, as far as I'm concerned and, a decimal representation of a number is nothing but a rational number or an irrational number, none of which are in Z, the set of integers,
(Z:={0,1,-1,2,-2,...}).
Now that we are familiar with the set we are working on, we need to prove that given any n in Z such that n is odd, then 3n+7 is even.
First of all, what does that mean? Well, if an even number is a number such that when we divide by 2 there is no remainder, i.e., is 0, then, an odd number is a number such that when we divide by two you have 1 as remainder (the remainder is a positive integer (Z^+=:{0,1,2,3,...}) such that is grater or equal to 0 and strictly less than the divident in order to have de division properly defined so, in our case, that remainder can only be 1 because we have reasoned that it can't be 0 or 2, because n is not even), althoug I would say that it's easier to understand (it can be proven (in fact, I let it to you as an exercise)) that if n is odd then n+1 is even and viceversa, so, given n odd, that means that it can be written as a multiple of 2 plus 1, i.e., n=2m+1 for some m in Z.
Now, following what you did, we substitute n in the given equation and we'll see that a factor of 2 can be extracted as a common factor and what we are left with is 2 times something that is in Z, hence, the given expression is, in fact an even number.
-How I would write the proof:
Let n be an odd integer, then, we want to show that 3n+7 is even.
If n in Z is odd then we can rewritte n as follows: n=2m+1 for all m in Z.
Now, we substitute our parametrized n in the given expression:
3n+7=
=3(2m+1)+7=
=6m+3+7=
=6m+10=
=2(3m+5) taking a common factor of 2 out.
We notice then that we have ended up with 2α, where α=3m+5 which is a number in Z.
Hence, 3n+7 is even for all n in Z such that n is odd. Q.E.D
If you have any doubt I'm more than happy to respond!!
@@davcaslop Thank you! I think I was thinking of it as more of a logic puzzle than a a rigorous process
Math sorcerer is there any way I could send you the download for the Calc 2 exam? When I put it in a UA-cam comment it gets deleted
Humanity has ten numbers (0, 1, 2, 3,...9)
Newton:
"0 is contingent" 🚫
and
"1-9 are necessary" 🚫
(this is the basis of Newton Calculus/Physics/Logic).
Leibniz:
"0 is necessary" ✅
and
"1-9 are contingent" ✅
(this is the basis of Leibniz Calculus/Physics/Logic).
Is zero the most important number?
Zero is the most important number in mathematics. Zero functions as a placeholder. Imagine a number, e.g., 5 and put as many zeroes behind it as you can think of. Zero drastically changes the value of the number from a mere 5 to 50, 500, 5000, 50000 and beyond.
Which is the greatest whole number?
There is no 'largest' whole number. Every whole number has an immediate predecessor, except 0. A decimal number or a fraction that falls between two whole numbers is not a whole number.
Why is it impossible to divide by zero?
The short answer is that 0 has no multiplicative inverse, and any attempt to define a real number as the multiplicative inverse of 0 would result in the contradiction 0 = 1.
Is 0 a rational number?
Yes, 0 is a rational number. Since we know, a rational number can be expressed as p/q, where p and q are integers and q is not equal to zero. Thus, we can express 0 as p/q, where p is equal to zero and q is an integer.
Is 0 A whole number?
The whole numbers are the numbers 0, 1, 2, 3, 4, and so on (the natural numbers and zero). Negative numbers are not considered "whole numbers." All natural numbers are whole numbers, but not all whole numbers are natural numbers since zero is a whole number but not a natural number.
Why is 0 a good number?
Zero helps us understand that we can use math to think about things that have no counterpart in a physical lived experience; imaginary numbers don't exist but are crucial to understanding electrical systems.
Zero also helps us understand its antithesis, infinity, in all of its extreme weirdness. 🔘 ♾ ☯️
Who is pushing Newtonian Calculus/Physics/Logic? The man was a moron (and a fraud who used political power to "win").
Our fundamentals are off because our fundamentals are directly "idiot" Issac Newton's fundamentals.
Our universe doesn't match Newton's illogical nonsense.
Theory of Everything is Cosmogony, Cosmology and Quantum and
Newton is buttcheeks at all three.
Nothing lines up.
Hard swap to Gottfried Leibniz.
Also, Aether > Gravity.
(Miller crushed Gravity so hard they had to wait more than a decade after his death to start weasling Newtonian logic a "win" again by burying Miller’s Aether theory).
Also, Tesla > Edison.
(3D height, 6D depth,
9D absorption i.e. contingent universe)
fundamental = rock
particular = sand
therefore God = dead, x>=y, hotel => trivago
The whole magic of the calculus thing is that their two processes lead them to exactly the same place. They can't be one right and one wrong, because at the end of the day, they have the same conclusions.
MS what’s the pencil your using ?
Ticonderoga
@@TheMathSorcerer
Just checked the price of this pencil in my country (Sri Lanka)
It cost my one month salary for a box of this pencil.. crazy
If n is odd then 3n is odd. And 3n +7 is sum of two odd numbers therefore it's even.
i mean odd times odd plus odd is even duh, why not just prove something more general?
I don't know what level this is intended for, but might as well mention, you have made implicit use of the distributive property, and more deviously, that arbitrary sums and products of integers remain integers (given integer k, 3k+5 is an integer). But again, I don't have the full context, and maybe you have already proven some things about the integers as a field, but even if you did, you certainly didn't invoke it here in this short. Usually an important point of these low-level proofs is to really scrape the bottom, to see, like, "oh wow I actually can't get there without assuming I'm in a field, I wonder if this only holds in fields", etc. Just assuming intuitive properties of arithmetic is like, if we were allowed to do this, I would assume the whole statement to be proven :P
❤Only for fans over 18 year⤵️ Alles sehr schön. Aber zuerst zusammen die Nummern 10 und 1. Eine Babymomm.beauty Brünette und eine andere Blondine. Es wäre unfair, wennu ich 4 wählen würde
if n is odd, 3n will always be odd (proof: basic intuition ie. 2n+n = even + odd = odd) => 3n+7 = odd + odd = even always. it's pretty fucking basic why even make a video about it lmao
Well it’s supposed to be trivial to make people understand basic proofs
imagine not understanding the importance of basic analysis in math and being condescending about it to others