If a/b = 0 then a=0

If a/b = 0 then a=0.
TRUE OR FALSE

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Can you repeat the question?

True

TRALSE

TRUE assuming b is actually a number and not some trick like division by infinity

true.

If a/b=0, b cant be infinit. Right?

technically if you divided something infinitely the fraction would shrink to zero (although never actually equating 0)
lrn2lim

In math you have to state your universe of discourse unless it's implied. I'm assuming a and b are in the reals. Then your statement is true.

True

a/b=0 implies a=0 for all values of b except infinity

a/b=0
a/0=b and 1/0 isinfinity
so b=infinite if a is not a 0 too

if b is a real number b can't be infinity
infinity isn't in the set of reals or the natural numbers

real numbers are a set of (-infinity to infinity)
and natural numbers a set of (1,infinity)

reals: (-infinity, infinity)

infinity is not a definite value like 1 or 2 or 3 ita a hypothetical term with no end hence the open bracket, but by saying real numbers lie from -infinity to infinity you refer to the fact that they can have "anyvalue possible" and if u say b=infinity u refer to the fact that b in reality is a value that cant be really defined hence the term "not defined" is commonly used, what i mean to say is when some one says b=infinity what they really mean is that its not defined,and do not refer to b having a definite value.

hope that clarifies your doubt.

For all b =/= 0 yes. This statement is true

That statement is true even if b=0, brainlet

0/0 = 0 ? who's the brainlet here

>if

>he doesnt know that the extended real numbers contain infinity as an element.

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>If a/0=0 then a=0
Looks like a true statement to me, brainlet

b=0 doesn't fall under the domain of a/b=0 idiot therefore it's irrelevant to the question. Pay attention to the if. The other guy you're arguing with is also retarded though he's completely wrong too.

Domain of this question is the reals, a/b=0 implies a=0 for all real a and b

b=0 is not irrelevant, if a/0=0 and a=0, the statement would be false. The case that b=0 still has to be considered. You don't even understand how basic implications work

It could be floored integer division on floating point numbers

>he extends the reals

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im mathematics you always need to say where you take a,b from. If a,b are real numbers and [math]b \neq 0[/math] of course it's true.

No, you don't understand implications.

The implication is:
Assume a/b = 0 is true
Then show a = 0 is true

We are taking a/b = 0 to be true. Any case where a/b != 0 doesn't matter.

It is analogous to the following implication: if today is friday then tomorrow is saturday.

>you: hahaha today is Thursday so I proved you wrong.

But infinitely small IS equal to zero.
Suppose you had to walk 1 meter in an infinite amount of time at a constant speed. The theoretical answer is to walk an infinitely small distance per second. However, once you've made progress, it's inevitable that you will finish before an infinite amount of time. Therefore you must move 0m/s. Infinitely small = 0

That's not true.

If infinitely small meant 0 then all integrals would be 0.

Infinity is the biggest number, so the inverse of infinity must be the smallest number. Since zero is the smallest number, 0 = 1/inf

That's what the original poster said, not what I said you dumbfuck. b=0 is still considered because it's a real number. When you consider b=0, the implication is a/0 implies a=0, which is still true. b=0 is within the domain of the question, not irrelevant

True IF b < 0 or 0 < b
If it is 0/0, then it's 1

>If it is 0/0, then it's 1

the current state of Veeky Forums

No its not the biggest number. Its not a number at all, the concept of something never-ending.

Assuming real numbers sure.
If b in infinity or some super massive number then a/b infinitely approaches 0 but doesn't reach it. Limits and shit.

[math]\text{Try }a=N\text{ with }b=\infty [/math]

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Nope because 0/0 =! 0, it is undefined.
We only care about b such that
a/b = 0 is true. Any time a/b != 0, the implication is true automatically.

Literally who means b=infinity means that's its undefined, name one single person who would use this absurd fucking notation, if it is anyone you know please kill that stupid fucking nigger. Who would use infinity to denote undefinededness, jesus christ that is most possibly the stupidest thing I've ever heard. Dear God please kill yourself holy fuck.

Let 1=0
A=1
QED

In what ring?

True for any algebra where multiplication is associative and multiplication by 0 annihilates (a*0 = 0 for all a).

[math]a/b=0[/math]
[math]ab^{-1}=0[/math]
[math]ab^{-1}b=0b[/math]
[math]a(b^{-1}b)=0b[/math]
[math]a1=0[/math]
[math]a=0[/math]

a/0 is undefined so a/0=0 is false. False implies anything is a true statement. You don't understand implications of you think (a/0=0 implies a=0) is false

Today is Friday implies tomorrow is Saturday. You consider every day of the week. Monday is Friday implies tomorrow is Saturday, true, Tuesday is Friday implies tomorrow is Saturday, true, etc. You check the whole domain of the question and verify that the implication holds for all elements in the domain. An implication is true if it looks like T implies T, F implies F, or F implies T. So you know the implication is true when the hypothesis is false or the hypothesis and conclusion are both true. Just because you checked that the hypothesis is false, doesn't mean you didn't consider it. You considered b=0 by checking that the hypothesis is false, your didn't consider b="red" because it's not in the donation of the question.

Engineer here. True if -inf

define a and b, that's high school stuff