(EDIT: Solved. I was on the right track with the border-collapse, but I had to use ctrl+f5 to see it)
Tried using border-collapse and border-spacing to remove them, but it didn't work.
Code:
<main>
    <div class="adminr1">
        <section class="adminc1">
            <table class="adminResults">
                <thead>
                    <td>cell</td>
                    <td>cell</td>
                </thead>
                <tr>
                    <td>cell</td>
                    <td>cell</td>
                </tr> 
        </table>
    </section>
    </div>
</main>
CSS:
 *
    {
        margin: 0;
        padding: 0;
        font-size: small;
        font-family: Roboto;
        vertical-align: middle;
        text-decoration: none;
    }
    main
    {
        font-size: 0;
        line-height: 1.5;
        text-align: center;
        margin: 0 auto;
        width: 86%;
        min-width: 1000px;
    }
    section
    {
        border: 1px solid #BBB;
        background: #FFF;
        border-radius: 7px;
        display: inline-block;
        overflow: hidden;
    }
    .adminr1
    {
        display: inline-block;
        width: 66%;
        height: 700px;
        margin-right: 5px;
        font-size: 0;
        margin-bottom: 10px;
    }
    .adminc1
    {
        width: 100%;
        height: 100%;
        font-size: 0;
    }
    /*Table Styles:*/
    .adminResults
    {
        width: 100%;
        border: 1px solid #000;
    }
    .adminResults thead
    {
        border: 1px solid #000;
    }
    .adminResults tr td
    {
        border-left: 1px solid #000;
        border-right: 1px solid #000;
    }
So far, this is the only page I have which uses a table, so I have no table-related styles anywhere else that could be blocking or overwriting the properties I'm trying to add, nor do i have any border-related files on other elements applied generally enough to do the same thing.
I'm obviously missing something, because this seems like it should be a very easy thing to do.
 
     
     
     
     
    