Functions blows up

[hhtt21]

If the function blows at a point, the limit of function does not exist. As a phrasal verb or even a mathematical term, blow up is confusing to me. Which one is it in the link?

Definition of blow up
transitive verb
1 : to build up or tout to an unreasonable extent

advertisers blowing up their products

2 : to rend apart, shatter, or destroy by explosion
3 : to fill up with a gas (such as air)

blow up a balloon

4 : to make a photographic enlargement of
5 : to bring into existence by blowing of wind

it may blow up a storm

intransitive verb
1 a : explode
b : to be disrupted or destroyed (as by explosion)
c : to lose self-control; especially : to become violently angry
2 : to become or come into being by or as if by blowing of wind
3 a : to become filled with a gas
b : to become expanded to unreasonable proportions
c : to gain a large amount of weight

In the ensuing two years Gibson blew up to more than 400 pounds as he ate an over-abundance of fast foods … —Tim Crothers

4 : to suddenly become very successful, prevalent, or popular

Latin-tinged pop is blowing up because it fits the musical times: … —Christopher John Farley

https://www.merriam-webster.com/dictionary/blow-up

 

[GoesStation]

When a function blows up, the speaker is imagining a little explosion.

 

[GoesStation]

I'm pretty sure the phrase the function blows up is widely used in physics and mathematics. I don't see anything childish about professionals using commonly-accepted shorthand. The "explosion" is just an analogy, a tool which gifted specialists apply frequently.

I see that the term has a specific definition in geometry, where those who use it are discussing a specific phenomenon. I'll have to ask my cousin who's a math professor at MIT whether his father, who was also a distinguished mathematician, worked in the area of math where this term would be used every day. I have a feeling he did, but I have only the vaguest idea of what these guys work on.

Here's a detailed discussion of how the term is used in various areas of math. As is so often the case, its meaning depends on context.

 

[hhtt21]

It's a childish way to say it, and a mature reader doesn't imagine any explosions. Clearly:

"lim(1/x) as x approaches zero" does not exist, or is said to be infinity. "lim(1/(x - 1) as x approaches one (1)" also doesn't exist.

As you can see, the use of 'blow up' only served to confuse you.

I supposed it is an idiom about for some cases in maths. I supposed it to be related to infinite growing of a function. My calculus text seems to be very professional one, McGraw-Hill and with 1260 pages plus 72 pages appendix plus 18 pages index at the back. The author introduces that expression in quotation marks. Maybe he might be trying to point out something figuratively, trying to construct a relation between the situation and one of the other meanings of "blow up". But it seems to me both odd and confusing.

 

[GoesStation]

By putting the expression in quotation marks, the author may be indicating that it's a casual way to describe the phenomenon in this case. Alternatively, he may be marking it as a new expression which he's about to define.

Take a close look at the name of the publisher, look up how to spell the name of the " mark, and review the rules for capitalizing subject pronouns.

 

[GoesStation]

You've corrected one spelling error. The post still has another one and a capitalization error.

 

[hhtt21]

By putting the expression in quotation marks, the author may be indicating that it's a casual way to describe the phenomenon in this case. Alternatively, he may be marking it as a new expression which he's about to define.

Take a close look at the name of the publisher, look up how to spell the name of the " mark, and review the rules for capitalizing subject pronouns.

I believe everything is fine now, but what was the problem with quotation? It was already correct.

 

[hhtt21]

By putting the expression in quotation marks, the author may be indicating that it's a casual way to describe the phenomenon in this case. Alternatively, he may be marking it as a new expression which he's about to define.

Take a close look at the name of the publisher, look up how to spell the name of the " mark, and review the rules for capitalizing subject pronouns.

If the last comment is correct in your link, the link given by Piscean is giving wrong info. Because they call it as "undetermined point", yours calls it as the point at which function goes to infinity, I think which is correct according to my text.

 

[GoesStation]

I believe everything is fine now, but what was the problem with quotation? It was already correct.

The first time I read your post, there was an extraneous a in the word.

 

[hhtt21]

The first time I read your post, there was an extraneous a in the word.

When I write, I usually in a hurry, and usually forget a proofread.

 

[GoesStation]

When I write, I'm usually in a hurry [no comma] and usually forget to proofread.

Please take more care when posting here.

 

[YAMATO2201]

It's a childish way to say it, and a mature reader doesn't imagine any explosions.

I wouldn't go so far as to say "childish". I'm guessing "blow up" is a casual way to describe a certain kind of discontinuity. (I'm assuming hhtt21 is not talking about algebraic geometry or the theory of differential equations.) By the way, if my memory serves me correctly, I have never seen "blow up" in any of my calculus/real analysis books (Spivak's Calculus on manifolds, Munkres' Analysis on Manifolds, Rudin's Principles of Mathematical Analysis, and Apostol's Mathematical Analysis). Is it commonly used in high school calculus texts published in the US?

The function f(x) = 1/x^2 'blows up' at x = 0. ;-)

 

[bubbha]

It just means that the function increases exceedingly rapidly. It may or may not involve infinity.

Take the TREE function for instance: TREE(1)=1, TREE(2)=3, and TREE(3) is so large that it dwarfs the unimaginably large Graham's Number. So the function "blows up".

 

[hhtt21]

) By the way, if my memory serves me correctly, I have never seen "blow up" in any of my calculus/real analysis books (Spivak's Calculus on manifolds, Munkres' Analysis on Manifolds, Rudin's Principles of Mathematical Analysis, and Apostol's Mathematical Analysis). Is it commonly used in high school calculus texts published in the US? The function f(x) = 1/x^2 'blows up' at x = 0. ;-)

See #6.

 

[YAMATO2201]

My calculus text

Please tell me its title and author.

 

[hhtt21]

Please tell me its title and author.

Robert T. Smith and Roland B. Minton by Mc-Graw Hill.

 

[YAMATO2201]

Robert T. Smith and Roland B. Minton by Mc-Graw Hill.

I see no title there.

 

[hhtt21]

I see no title there.

What do you mean by "I see no title there"? By there, do you refer to the website of Mc-Graw Hill?

 

[teechar]

No. You did not provide the title in post #20.

 

[hhtt21]

No. You did not provide the title in post #20.

Unfortunately, I have already assumed the title and context is known. The title is Calculus [Early Transcendental Functions]. I have also supposed I mentioned the name and context in the flow of the thread. Sorry for it.