How do I use display style in running text?

Question

I'm writing my thesis. Problem is that when I type the following mathematical expressions inside the equation environment and outside it, I get a different style of the same mathematical expressions:
A population $N(t)$ is said to be persist (or strongly persist) 
if $N(0)> 0$ implies $N(t) > 0$ and $liminf_{ttoinfty}{N(t)} > 0$

or
begin{equation*} 
liminf_{ttoinfty}{N(t)} > 0 
end{equation*}.

Why does the command liminf_{ttoinfty} look differently in each case? I need to use both version i.e. in text and inside equation. But I want it to look same everywhere.

Mico · Answer

You asked,

Why does the command liminf_{ttoinfty} look differently in each case?

What you have "discovered" is that inline-math and display-math typesetting conventions differ in several ways. This difference is not a problem. Instead, it is a typesetting convention that has evolved and stood the test of time over decades (centuries?) of typesetting practice.
If you absolutely feel like you have to override TeX's default settings for typesetting inline math material, you may do so quite easily, by inserting displaystyle directives after initiating inline math mode.
Just be prepared to have to accept inferior typographic results, as the line spacing within a paragraph will look highly uneven. To wit, compare the two three-line paragraphs in the following screenshot. In the first paragraph, the distance between lines 1 and 2 is the same as between lines 2 and 3. This is decidedly not the case in the second paragraph, which employs two displaystyle directives. I'm fully aware of the saying that there's no arguing about tastes. Nevertheless, I would posit that the first paragraph is superior, typographically speaking, to the second.

documentclass{article}
setlengthparindent{0pt} % just for this example
begin{document}
hrule 
A population $N(t)$ is said to be persist (or strongly persist) 
if $N(0)> 0$ implies $N(t) > 0$ and $liminf_{ttoinfty}{N(t)} > 0$.
A population $N(t)$ is said to be persist (or strongly persist) 
if $N(0)> 0$ implies $N(t) > 0$ and $liminf_{ttoinfty}{N(t)} > 0$.
hrule
A population $N(t)$ is said to be persist (or strongly persist) 
if $N(0)> 0$ implies $N(t) > 0$ and $displaystyleliminf_{ttoinfty}{N(t)} > 0$.
A population $N(t)$ is said to be persist (or strongly persist) 
if $N(0)> 0$ implies $N(t) > 0$ and $displaystyleliminf_{ttoinfty}{N(t)} > 0$.
hrule
end{document}

How do I use display style in running text?

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