(1)
show true for a=1
1+b=b+1
subtract 1 both sides
b=b true
(2)
assume true for a=n
n+b=b+n
(3)
show true for a=n+1
n+1+b=b+n+1
subtract 1 both sides
n+b=b+n
true by (2) thus holds for all values of a
(1)
show true for a=1
1+b=b+1
subtract 1 both sides
b=b true
(2)
assume true for a=n
n+b=b+n
(3)
show true for a=n+1
n+1+b=b+n+1
subtract 1 both sides
n+b=b+n
true by (2) thus holds for all values of a
"If a² is even, a is even" - if a²=2, a is 1.41421...., so that's disproven
a=0.(9)
a<1
2a<2
Welcome to what happens when you follow the rules of Maths and use a symbol for a non-terminating number
"If a² is even, a is even" - if a²=2, a is 1.41421...., so that's disproven
a=0.(9)
a<1
2a<2
Welcome to what happens when you follow the rules of Maths and use a symbol for a non-terminating number
"simple case (like the addition of rational numbers) are demonstrable" - demonstrable in all cases by using Cuisenaire rods
"simple case (like the addition of rational numbers) are demonstrable" - demonstrable in all cases by using Cuisenaire rods
"produces an infinite sequence" - which is why the rule is don't substitute any values for the symbols until the final step 🙄
"pi +e is simply pi+e" - or e+pi. a+b=b+a, a=pi, b=e
"produces an infinite sequence" - which is why the rule is don't substitute any values for the symbols until the final step 🙄
"pi +e is simply pi+e" - or e+pi. a+b=b+a, a=pi, b=e
"Prove that" - you can't do arithmetic with non-terminating numbers. This is why we use symbols for them, and don't substitute any numerical value for them, if at all, until the last step. These are established rules.
"Prove that" - you can't do arithmetic with non-terminating numbers. This is why we use symbols for them, and don't substitute any numerical value for them, if at all, until the last step. These are established rules.
LHS=2+3
=(1+1)+(1+1+1)
=1+1+1+1+1
=(1+1+1)+(1+1)
=3+2
=RHS
Therefore 2+3=3+2 QED
The real beauty of Maths is being able to prove things are true
LHS=2+3
=(1+1)+(1+1+1)
=1+1+1+1+1
=(1+1+1)+(1+1)
=3+2
=RHS
Therefore 2+3=3+2 QED
The real beauty of Maths is being able to prove things are true
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